The two-sample t-test is one of the most commonly used hypothesis tests in Six Sigma, a methodology for process improvements, work. It is applied to compare whether the average difference between two groups is really significant or if it is due instead to random chance. Select an application of the two-sample t-test and describe how it was justified to use the t-test for this particular application. Describe what the P-value of the 2-sample t-test of your example in part (1) means. Note that you are not being asked to provide a general definition of the P-value in hypothesis testing problems. You are being asked to interpret the P-value in the context of the particular example that you have selected.


Happy Pi Day!
Tomorrow is March 14, 2015 or 3/14/15.
Geeks, math wizards and even, PiiComm employees, are very excited about this Saturday – it’s Pi Day. Pi Day is the celebration date of the number that is the ratio of a circle’s circumference to its diameter.
The celebration is held annually on 14 March, because 3/14 spells out the first three digits of π, or pi, which is 3.14. But it’s not just any Pi Day.
This year is the first time in a century that the date is 3/14/15, which describes the first five digits of pi, 3.1415. Mass elation will peak at 9.26:53am when the date and time will describe pi to 10 digits.
Although PiiComm has been in business for less than 100 years we look forward to celebrating again in 2115!
Happy PiiComm day!


Department of Mathematics
The Mission of the Mathematics Department of Kaskaskia College is to provide quality instruction in mathematics to all students as well as offer mathematics courses that will support other departments and programs in the college.
- To provide a learner-centered environment that addresses the diverse needs of our learning community.
- To provide an educational program that enhances the development of critical thinking, problem-solving, computational, and active learning skills essential for responsible decision-making and a broad range of careers.
- To provide the major sequence courses for students intending to transfer in Mathematics, Science, Computer Science, Engineering, and the Health professions.
- To encourage exploration and evaluation of innovative approaches to teaching mathematics


Welcome to My Home Page
My name is John Sung Lee. I am a mathematician and a physics aficionado.
My research interests largely lie in Geometry and Physics. I am also dabbling in Number Theory, particularly Analytic Number Theory (it's such a beauty!) and in Quantum Computing, particularly Computational Complexity problems associated with it.
I received my Ph.D. in Mathematics (Differential Geometry) from the University of Connecticut in 2002, supervised by Professor Kinetsu Abe. I have been employed by the University of Southern Mississippi since 2001.


Our poetry folder is a perfect example how we do the above two activities. We highlight word wall words, words we can read, or words that tell about the poem. Then we highlight word chunks within the poem.
Click the next link to learn more info about word chunks.
We are getting a lot of hands-on learning with our new math curriculum, Investigations. Many of us teachers have some familiarity with the program as it was previously named TERC units--which is reputed to be lots of hands-on minds-on learning of math.
The curriculum has a series of smartboard interactive activities. Here we are playing "Build it to 20." We open a card and use the pennies to make 20 using 2 sets of ten frames. It was interesting to note the strategies of how students built their 20. We made a chart and shared our strategies. Love the math talk...
skip count by 5s
make a 10 (then count on like 10 and 2 to make 12)
know how much is left (18 is 2 less than 20, so fill it up and leave 2 extra spots).
pattern blocks (and not picture were linking cubes, and geoblocks.). Lots of nice cooperative play, by the way!


Department Head – Ms. S. Joseph
The main aims of teaching mathematics in school are to enable students to solve mathematical problems of daily life. In our school which is affiliated to Cambridge University the subject is compulsory for all students from year 7 to 11. From year 7 to 9 all students do the same course in maths.
From year 10 onwards they branch out into extended and core maths depending on their selection of vocations and taste for the subject.
We offer mathematics at Advanced Level (A) also. AS and A level each consist of a course in mathematics and another in statistics. As a department we aim at preparing a sound foundation needed for various vocations for further learning in maths and related subjects. We try to create a good understanding of the subject which would develop the rational and scientific attitude towards life.


In this video we will learn how to solve the complex Navier-Stokes equations, within power bound of your PC. Here concepts of RANS and FVM are introduced in a logical manner.
Detailed description of video lecture is given below.
Actual Vs Averaged Solution
As we discussed in previous article, exact solution of N-S equations is too much of accuracy.It captures every minute details of turbulent flow. But an engineer is not interested in such a solution, what he needs is an averaged solution as shown below.This is in fact averaged solution of actual solution.
Fig.1 Actual Vs Averaged solution
Any variable in a turbulent flow can be represented as sum of mean value and fluctuating value. An example is given below for variable u.
Where averaged quantity is found out using following operation.
Here time interval of integration should be carefully selected. It should be small enough to capture any unsteadiness in flow, at the same time it should be big enough to smooth out fluctuations due to turbulence. A pictorial representation of averaging operation is shown below.
|Fig.2 Averaging operation done on a turbulent flow|
How to obtain averaged solutions ?
To obtain this averaged values, instead of solving actual N-S equations we can solve something called, averaged N-S equations. Navier Stokes equations generated after averaging operation is known as, Reynolds averaged Navier Stokes equations.
Fig.3 Conversion of Navier-Stokes equations to Reynods Averaged N-S equations using averaging operation
The averaged equations are represented here in index notation form. Here F represents external force acting on fluid.
Reynolds Stress – Turbulence Modeling
But RANS is not purely in terms of mean values. The last term of RANS is in terms of fluctuating components. This term is known as Reynolds stress.
There are various turbulence models available in order to represent, Reynolds stress in terms of mean quantities. Selection of proper turbulence model is one of the most important step in a CFD project.
Solving RANS numerically
RANS is not so difficult to solve numerically. Current CFD packages use mainly 3 numerical methods. They are FEM, FDM and FVM. Some commercial packages using these methods are listed here.
Fig.4 Different numerical schemes used in CFD and some commercial CFD packages using them
It is clear that FVM (Finite Volume Method) is the most common method of all. So in this article we will concentrate only on FVM.
Finite Volume Method
The fundamental flow equations are derived in FVM, using integral approach. Here instead of considering a differential volume we will consider a finite volume of arbitrary shape. And we will say that when flow passes through it, rate of increase of quantity inside the volume will be same as flux in minus flux out, plus generation of quantity.
Fig.5 Basic philosophy of FVM : Conservation of quantity
You can apply this to any quantity. Quantity can be either mass or momentum component. Such a concept will lead to conservative equations in integral form. It will have general form like this.
Where U represents quantity. So we can apply this general form to mass, so U will be density in to velocity. It will lead to conservation of mass equation. Similarly we can apply it for 3 components of momentum. We will get 3 more equations, which are conservation of momentum equations. So again we have 4 equations in total. This time in integral form.
Now the challenge is to solve these equations throughout the control volume numerically. Here there are surface and volume integrals. We will execute numerical integration of these equations on small non overlapping cell volumes, of arbitrary shape. So before executing numerical integration, actual control volume is split into small cells, as shown below.
Fig.6 Conversion of Control volume in to small non-overlapping cells : Meshing
This process is known as meshing. There are various meshing schemes available in CFD.
Now we need to execute surface and volume integrals on these cells. Such a cell is shown here. The method of surface and volume integrals are also shown pictorially.
Fig.7 Numerical approximation of volume and surface integrals in FVM
In FVM volume integrals are approximated as volume of cell multiplied by average value of quantity at centroid of cell. Similarly surface integrals are approximated as midpoint averaged values. So for this cell we have to do same operation on all four surfaces. Now we can apply same operation throughout the cells. This will generate series of equations in terms of averaged values. We can solve them together, with help of some boundary condition. An appropriate mathematical solver will do this task for you. Usually CFD solvers use iterative method to get the solution.
CFD at a Glance
The steps we have explained so far are summarized here in step by step manner.
Fig.8 Step by step CFD procedure
Before winding up the lecture, we will also see a sample CFD problem.
Fig.9 A sample CFD problem
How to build a career in CFD?
Hope you got a good introduction to CFD from here. Now its time to get hands on experience on CFD packages. Most used CFD packages in industry and its relevance are given below.
- ICEM CFD – A perfect software to do meshing
- Gambit – Another meshing software, but has become obsolete nowadays
- Fluent – Most preferred CFD solver in industry
- CFX – Another good solver
- Icepak – Electronics thermal management
Now it is clear from range of CFD packages available in market that, it is not possible to learn all of them at a stretch. So first thing you have to do is to find out your area of interest and select a good CFD package which will suit your need. You will be able to produce colorful results from CFD, but the real challenge is in understanding physics behind the problem ( make sure you are good in fluid mechanics and mathematics ). Please keep in mind that most of the time CFD produces rubbish results. Reasons might be poor quality of mesh, wrong physics used in CFD solver, wrong solver selected or wrong boundary condition applied. So it is imperative to spend lot of hours running simulation and analyzing results of simulation in order to become a good CFD engineer.


MS Math - Mr. Goffner
Hello and welcome to 8th Grade Math. My name is Mr. Goffner, and I am very passionate about helping my students to achieve their goals in math, including achieving the highest possible score on the state exam and achieving the highest possible score on the SHSAT so that they may get into the high school that they dream of. Myself being a graduate of Bronx High School of Science, I know what it takes for success on the entry exam. I received a B.S. from The George Washington University and an M.S.Ed. from CUNY-Queens College. I am currently in my second year of teaching at OWNCS and had four years of teaching experience prior to joining the OWNCS family. I am having an excellent time and will stop at nothing to make a positive impact on the school and on the community.
Units for the 8th Grade Mathematics curriculum include: Exponents and Scientific Notation, Graphs and Functions, Multi-step Equations, Graphing Lines, Data and Predictions, Systems of Linear Equations, Geometric Transformations, Sum of Interior Angles, and Measurement and Geometry.
Together we can make this a wonderful school year.p>


Fractals are geometrical objects which create a reduced self-sized copy of the object which they originate from. The geometric pattern is repeated at smaller scales, and it is eventually turned into an irregular shape which cannot be measured or represented by classical geometry. Fractals are primarily applied in computer modeling, where they are used for a better understanding of certain structures found in nature.
In fact, fractals came to be a part of natural sciences when it was observed that some nature objects display properties of a fractal - they are complex shapes with self-similarity in their structures. Although a segment of a natural fractal structure may not be perfectly identical with other parts of that structure, it does match closely when put under the microscope.
These geometrical objects can be self-similar when the scale of magnification is changed for one of them. For example, a river and its tributaries may loosely follow a fractal structure, wherein every tributary has its own tributaries. Therefore, it has a similar structure as the river, even though it covers a smaller area.
Other nature structures where you will find self-similar structures are mountain ranges, clouds, crystals, lightning, broccoli, cauliflower, pulmonary vessels, blood vessels, and snow flakes. Other examples in nature include a coastline with numerous peninsulas and inlets, the structure of a galaxy, and the distribution of galaxies in our universe. In economics, the rise and fall can be fractals too, when they are plotted as a function of time. Even within our own bodies, there are instances of fractals, including the branching of the blood vessels, bronchioles, and nerves.
The triadic Koch curve is one of the methods by which a fractal can be constructed. With this method, a straight segment is drawn. Then, it is divided into three identical parts, where the central part is substituted by two similar pieces. Consequently, four segments are created. The same procedure is applied on each of the four segments, and it is repeated for an infinite number of times. The resultant curve creates the distinctive self-similar pattern known as a Koch Curve.
The fractal concept is often used by physicists for analyzing the properties of amorphous solids as well as rough interfaces. It can also be used in the study of the dynamics of turbulence as well as the dynamics of population. In medicine, fractals are deployed to analyze heart rhythm and blood circulation. In computer graphics, compressing a large amount of visual information is rendered effectively by identifying the commonly occurring fractals in that scene, and those fractals are reconstructed to arrive at a shape which closely resembles the original nature scene.
More About Fractals:


IcyData now has Corsi and Fenwick calculation in its live parsing.
Now that the job of populating past games is done, I can have IcyData calculate in real-time going forward.
I’ve got some ideas for my next viz and will hopefully have that out soon.
IcyData is now collecting data on corsi and fenwick values on a per game basis for every player.
It shouldn’t take more than a couple hours to accumulate all the data and then I’ll work on coming up with a decent way of showing it.
I’d also like to create a Viz showcasing them and see if I can’t get any insights out of the data.


Answer: After a whole lot of taper.
John Hussman has a famous graph of short rates plotted against the ratio of monetary base to GDP. I’ve never seen anyone plot the same for long rates, so I did it:
Recently Base/GDP has been about 0.22, so we are way out on the right end tail. It would take a reduction of the ratio of about 15 percent of GDP to begin to raise long rates, or about $2.6 trillion at current rates of GDP. The St. Louis base is currently at $3.7 trillion, and has been growing at over 20 percent a year since the last recession.


Book VI applies the theory of proportion from Book V to similar figures and presents the geometrical solution to quadratic equations. Since the ancients recognized four or five elements at most, Plato sought a small set of uniquely defined geometrical objects to serve as elementary constituents.
The philosopher Immanuel Kant 's treatment of human knowledge had a special role for geometry. Theology was also affected by the change from absolute truth to relative truth in the way that mathematics is related to the world around it, that was a result of this paradigm shift.
Desargues saw that he could prove them all at once and, moreover, by treating a cylinder as a cone with vertex at infinity, demonstrate useful analogies between cylinders and cones.
Furthermore, since the substance of the subject in synthetic geometry was a chief exhibit of rationality, the Euclidean point of view represented absolute authority.
A determination of the height of a tower using similar triangles is demonstrated in the figure. Triangles with three equal angles AAA are similar, but not necessarily congruent. However, the Egyptian scribes have not left us instructions about these procedures, much less any hint that they knew how to generalize them to obtain the Pythagorean theorem: And the main subject of later Greek geometry, the theory of conic sectionsowed its general importance, and perhaps also its origin, to its application to optics and astronomy.
Fermat's tangent methodPierre de Fermat anticipated the calculus with his approach to finding the tangent line to a given curve. The ancient Greek geometers soon followed Thales over the Bridge of Asses. Similarly, eagerness to know the volumes of solid figures derived from the need to evaluate tribute, store oil and grain, and build dams and pyramids.
Another example is al-Tusi's son, Sadr al-Din sometimes known as "Pseudo-Tusi"who wrote a book on the subject inbased on al-Tusi's later thoughts, which presented another hypothesis equivalent to the parallel postulate. A second geometrical inspiration for the calculus derived from efforts to define tangents to curves more complicated than conics.
The Bridge of Asses. Geometry was too prolific of alternatives to disclose the true principles of nature. Since the publication of Euclid's Elements circa BCE, many geometers made attempts to prove the parallel postulate. The number of rays in between the two original rays is infinite.
Apollonius introduced the terms ellipse, hyperbola, and parabola for curves produced by intersecting a circular cone with a plane at an angle less than, greater than, and equal to, respectively, the opening angle of the cone. Other useful models of hyperbolic geometry exist in Euclidean space, in which the metric is not preserved.
Among the jewels in Book XII is a proof of the recipe used by the Egyptians for the volume of a pyramid.Properties Relation to Euclidean geometry. Hyperbolic geometry is more closely related to Euclidean geometry than it seems: the only axiomatic difference is the parallel currclickblog.com the parallel postulate is removed from Euclidean geometry the resulting geometry is absolute currclickblog.com are two kinds of absolute geometry, Euclidean and hyperbolic.
Properties Relation to Euclidean geometry. Hyperbolic geometry is more closely related to Euclidean geometry than it seems: the only axiomatic difference is the parallel currclickblog.com the parallel postulate is removed from Euclidean geometry the resulting geometry is absolute currclickblog.com are two kinds of absolute geometry, Euclidean and hyperbolic.
COLLEGE OF ARTS & SCIENCES MATHEMATICS Detailed course offerings (Time Schedule) are available for. Autumn Quarter ; Winter Quarter ; MATH Intermediate Algebra (0) Intermediate algebra equivalent to third semester of high school algebra.
Includes linear equations and models, linear systems in two variables, quadratic equations, completing the square, graphing. In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean currclickblog.com Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises when either the metric requirement is relaxed, or the parallel postulate is replaced with an alternative one.
Introduction to Hyperbolic Geometry Julien Paupert Spring 1. Contents Geometry of real and complex hyperbolic space The hyperboloid model Let n>1 and consider a symmetric bilinear form of signature (n;1) on the vector space Rn+1, e. g. the standard Lorentzian form. This note is intended for students who have a background in multivariable calculus and some experience in proof-based mathematics.
Topics covered includes: Euclidean geometry, Polygons, Triangulations and Tilings, The Chord Theorem, Tangrams and Scissors Congruence, Spherical Geometry, Hyperbolic geometry, Euclids axioms and the parallel postulate, Incidence geometry and Hyperbolic isometries.Download


Hex to Ascii (String) Converter
To use this hex to string converter, type a hex value like 6C 6F 76 65 and into the left field below and hit the Convert button. You will get the according string.
Hexadecimal System (Hex System)
The hexadecimal system (shortly hex), uses the number 16 as its base (radix). As a base-16 numeral system, it uses 16 symbols. These are the 10 decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and the first six letters of the English alphabet (A, B, C, D, E, F). The letters are used because of the need to represent the values 10, 11, 12, 13, 14 and 15 each in one single symbol.
Hex is used in mathematics and information technologies as a more friendly way to represent binary numbers. Each hex digit represents four binary digits; therefore, hex is a language to write binary in an abbreviated form.
Four binary digits (also called nibbles) make up half a byte. This means one byte can carry binary values from 0000 0000 to 1111 1111. In hex, these can be represented in a friendlier fashion, ranging from 00 to FF.
In html programming, colors can be represented by a 6-digit hexadecimal number: FFFFFF represents white whereas 000000 represents black.
ASCII (American Standard Code for Information Interchange) is one of the most common character encoding standards. Originally developed from telegraphic codes, ASCII is now widely used in electronic communication for conveying text.
As computers can only understand numbers, the ASCII code represents text (characters) with different numbers. This is how a computer ‘understands’ and shows text.
The original ASCII is based on 128 characters. These are the 26 letters of the English alphabet (both in lower and upper cases); numbers from 0 to 9; and various punctuation marks. In the ASCII code, each of these characters are assigned a decimal number from 0 to 127. For example, the ASCII representation of upper case A is 65 and the lower case a is 97.
Hex to Ascii (String) Conversion
The string for a given hex number will depend on the programming language of the string. Theoretically you can invent your own alphabet and language, encode it and produce strings.
In ASCII, which is one of the most common encoding systems, a few conversion examples are as follows:
48 65 6C 6C 6F = Hello 68 65 6C 6C 6F = hello 47 6F 6F 64 20 6D 6F 72 6E 69 6E 67 = Good morning 6C 6F 76 65 = love 4C 6F 76 65 = Love


Blaze and the Monster Machines
In Blaze and the Monster Machines magazine, children can enjoy high-speed adventures with their favourite monster trucks. Based on the award-winning Nickelodeon series, every action-packed issue features an exclusive branded gift, interactive stickers, two easy-to-read stories, colouring, puzzles, recipes and crafts. Each learning activity is focused on the STEM subjects of science, technology, engineering and maths, encouraging little ones to learn about problem-solving in the key areas.
Click here to buy now!
Pre-school children, aged 3-7 years


Second graders are expected to be fluent with their recall of math facts with sums up to 20. They must also use their knowledge of place value to add and subtract within 100 using various strategies. Subitizing usually starts out small, but over time, according to Douglas Clements (1999), provides "stepping-stones to constructing more sophisticated procedures with larger numbers" (pg. 401). Virtual manipulatives, apps, and SMART Table activities pose a familiar setting for children as they are used to playing games either online or through handheld devices.
Visit https://www.smore.com/5m82s or view below:
Clements, D. H. (March 1999). "Subitizing: What is it? Why Teach it?" Teaching Children Mathematics. Retrieved from http://gse.buffalo.edu/fas/clements/files/subitizing.pdf


I’m very happy to announce that our CMS department faculty search is live. As in previous years, we’re searching broadly — truly broadly. We’re looking across applied math and computer science both and expect to be able to make multiple offers. We’re interested in candidates in a variety of core areas, from distributed systems and machine learning to statistics and optimization (and lots of other areas). But, more generally, we look for impressive, high-impact work rather than enforcing preconceived notions of what is hot at the moment. Beyond the core areas of applied math and computer science, we are hoping to see strong applications in areas on the periphery of computing and applied math too — candidates at the interface of EE, mechanical engineering, economics, privacy, biology, physics, etc. are definitely encouraged to apply! As I said in my recent post, inventing new CS+X fields is something that Caltech excels at — it’s our brand.
I’m happy to announce that Caltech will be continuing its growth in Computing & Mathematical Sciences (CMS) this year. The ad is now officially up. Please spread the word!
The search will be considering strong applications from anywhere within Applied Math and Computer Science, since Caltech likes to hire based on impressive and high-impact work, rather than a preconceived notion of what area is interesting at the moment. Quoting from the ad: “Research areas of particular interest include applied mathematics, computational science, as well as computing.” You can’t get much broader than that! (I personally really hope to see some strong candidates in statistics, networked/distributed systems, and security/privacy, so if you’re from any of those areas and are on the fence about applying — please do!)
Also, for those EE folks out there, don’t let the fact that your degree isn’t in CS or Applied Math deter you from applying. Caltech has a very fuzzy interpretation of the boundaries between disciplines — many folks have joint appointments between CMS and EE, and many CMS faculty advise EE students (and vice versa).
I’m happy to announce that Caltech will be looking for faculty applicants in Electrical Engineering this year. Go here to see the official ad and to apply. For various reasons the announcement is going up late, so I hope that this will help to spread the word quickly…
The search will be looking for strong applicants from anywhere in EE systems, since Caltech likes to hire based on impressive and high-impact work, rather than a preconceived notion of what area is interesting at the moment. But, I think it’s fair to say we have a particular need on the networking / wireless side of things and the machine learning side of things. Also, there is a growing interest in power systems and energy issues. So, if you’re from any of those areas and you’re on the fence about applying, please do! But, the search is certainly not limited to those areas. Quoting from the ad: “research areas of interest include, but are not restricted to, signal processing, communications and information theory, control systems, networks, optimization, machine learning, large data systems, power systems, robotics and autonomous systems and cyber-physical systems.”
Also, if you have a degree from a department other than EE, don’t let that stop you from applying — Caltech has a very fuzzy interpretation of the boundaries between disciplines. While I’m not officially in EE, there are strong ties between EE systems and CS, as well as between EE systems and Applied & Computational Math (ACM) and Control and Dynamical Systems (CDS). Actually, the first two students that I graduated were EE students co-advised with EE faculty, and about half of the students in our RSRG group today are EE students. So, this is the next best thing to CS having a search, which unfortunately, we don’t this year (grumble, grumble).


Euclidean Geometry is actually a study of plane surfaces
Euclidean Geometry, geometry, is a really mathematical examine of geometry involving undefined phrases, for illustration, factors, planes and or lines. Regardless of the very fact some investigation results about Euclidean Geometry had by now been finished by Greek Mathematicians, Euclid is highly honored for creating an extensive deductive structure (Gillet, 1896). Euclid’s mathematical method in geometry chiefly based on offering theorems from a finite quantity of postulates or axioms.
Euclidean Geometry is basically a examine of plane surfaces. Nearly all of these geometrical principles are readily illustrated by drawings with a piece of paper or on chalkboard. A really good variety of ideas are commonly identified in flat surfaces. Illustrations embrace, shortest length in between two details, the idea of the perpendicular to your line, and also the thought of angle sum of a triangle, that usually adds around a hundred and eighty degrees (Mlodinow, 2001).
Euclid fifth axiom, generally identified as the parallel axiom is described inside the next method: If a straight line traversing any two straight lines forms interior angles on 1 aspect fewer than two ideal angles, the 2 straight lines, if indefinitely extrapolated, will meet up with on that same facet wherever the angles smaller compared to the two proper angles (Gillet, 1896). In today’s mathematics, the parallel axiom is simply stated as: through a position outside the house a line, there may be just one line parallel to that particular line. Euclid’s geometrical principles remained unchallenged until such time as round early nineteenth century when other concepts in geometry begun to arise (Mlodinow, 2001). The brand new geometrical principles are majorly referred to as non-Euclidean geometries and they are put to use because the solutions to Euclid’s geometry. As early the durations within the nineteenth century, it is actually not an assumption that Euclid’s principles are beneficial in describing the many physical space. Non Euclidean geometry serves as a form of geometry that contains an axiom equivalent to that of Euclidean parallel postulate. There exist a considerable number of non-Euclidean geometry groundwork. Most of the illustrations are described beneath:
Riemannian geometry can be known as spherical or elliptical geometry. This sort of geometry is called following the German Mathematician via the title Bernhard Riemann. In http://buyessay.net/thesis-proposal 1889, Riemann determined some shortcomings of Euclidean Geometry. He found the give good results of Girolamo Sacceri, an Italian mathematician, which was complicated the Euclidean geometry. Riemann geometry states that when there is a line l and a stage p outside the line l, then there’re no parallel strains to l passing by using issue p. Riemann geometry majorly promotions together with the analyze of curved surfaces. It will probably be said that it’s an improvement of Euclidean thought. Euclidean geometry can’t be used to analyze curved surfaces. This way of geometry is directly connected to our everyday existence considering the fact that we are living on the planet earth, and whose floor is actually curved (Blumenthal, 1961). A number of concepts over a curved surface area seem to have been brought forward via the Riemann Geometry. These principles comprise, the angles sum of any triangle on a curved area, which is certainly acknowledged to always be greater than one hundred eighty degrees; the reality that there can be no strains on the spherical area; in spherical surfaces, the shortest length relating to any provided two details, generally known as ageodestic isn’t special (Gillet, 1896). For illustration, you will find several geodesics amongst the south and north poles on the earth’s floor which can be not parallel. These strains intersect within the poles.
Hyperbolic geometry is usually named saddle geometry or Lobachevsky. It states that when there is a line l in addition to a level p outdoors the road l, then there’re a minimum of two parallel lines to line p. This geometry is named for any Russian Mathematician through the title Nicholas Lobachevsky (Borsuk, & Szmielew, 1960). He, like Riemann, advanced to the non-Euclidean geometrical ideas. Hyperbolic geometry has a considerable number of applications with the areas of science. These areas encompass the orbit prediction, astronomy and house travel. For example Einstein suggested that the room is spherical because of his theory of relativity, which uses the ideas of hyperbolic geometry (Borsuk, & Szmielew, 1960). The hyperbolic geometry has the subsequent principles: i. That you’ll discover no similar triangles with a hyperbolic place. ii. The angles sum of a triangle is fewer than 180 degrees, iii. The floor areas of any set of triangles having the identical angle are equal, iv. It is possible to draw parallel lines on an hyperbolic place and
Due to advanced studies inside of the field of mathematics, it really is necessary to replace the Euclidean geometrical ideas with non-geometries. Euclidean geometry is so limited in that it is only valuable when analyzing some extent, line or a flat floor (Blumenthal, 1961). Non- Euclidean geometries may very well be accustomed to review any type of area.


in a enough math smart get i am to phd
Signed, a good-but-not-great math student who got a math PhD almost 20 years ago. I'm about to finish my undergraduates studies; I majored in mathematics and minored in physics, and I always intended on going to grad school to pursue a PhD in mathematics, but I've been having doubts recently. I think you probably should, but consider your situation and wants carefully before you decide. Anywho, I know plenty of students that hated math at one point, but once they reach multivariate. There's actually a movement of revamping the way math is taught, to get kids to enjoy it. 30.09.2018 · Having a PhD in mathematics gives those seeking such a position the education required, and through having a background in mathematics, recent …. level 1. One does not “get” a PhD by hanging around in the system for a bunch of years. Tanya Golash-Boza July 21, 2011 at 2:24 PM. 31.07.2014 · The first question I ask students who genuinely wonder whether you have to be smart to become a PhD, is whether they are considering to become a PhD themselves, or just think I …. verplichte keuring cv-ketels op gas
The Red Queen Matt Ridley Chapter Summary
PhD, Atmospheric Science 23 points · 4 years ago. But, you also Autor: Tanya Golash-Boza How to Get a PhD in Mathematics | The Classroom Diese Seite übersetzen https://www.theclassroom.com/phd-mathematics-7975418.html Often, you do not need a doctorate or Ph.D. .requires years worth of study and focus, as well as a high ability to solve problems. Replies. Earning a Ph.D. You just have to be "smart enough", and be very very persistent. "You are smart enough, so let's get to work." Reply Delete. I've always seen PhD students as those students who get A in every course and that I might not be able to do a PhD because of this. in order to have a successful career in the math world, but having a Ph.D. Straight-A students pursue PhDs, but not every PhD. Searching for a Program. 12.07.2014 · A PhD in Mathematics is not somehow making a person unemployable. A lot of students tend to dislike math in the beginning since they become discouraged because of the way it is taught.
Introduction For Inventory System Thesis
essay about the west philippine sea “Getting” a PhD. Unlike Bachelor’s and Master’s degrees where the majority of the requirement is to complete coursework. In academia, it is true you have to put in the hours to get results. Jonathan: I also like how Gladwell talks about "luck." Many of the successful people he talks about were lucky enough to have the right opportunities and meet the right people. Reply. from an accredited and renowned university will help establish your name in the field. Anyway, you're obviously quite bright if you're acing your analysis and algebra (I'm assuming linear or abstract algebra?) classes, so that will help. 10.12.2010 · I do love what I am studying; but, I sometimes begin to think that maybe I am not smart enough to get into a PhD program--which is what I had planned on pursuing after the completion of my undergraduate degree (because of the grades) Yes this is true, but liking math is something that comes as you get better at it. It just means that the type of employment one will find is different. I did well in all my courses (3.92 GPA), but I'm trying to seriously consider if my background is strong enough now and if I'd truly have the motivation to stick it out.
Thanks, Dave! I've also been.
- volpone opening speech analysis essay
- literature review on demat services
- sample letter of recommendation for ordination
Latest posts by (English is a crazy language essay introduction)
- Am I Smart Enough To Get A Phd In Math - December 14, 2020
- 2018 FIFA World Cup Match Prediction: Sweden vs. England - July 5, 2018
- 2018 FIFA World Cup Match Prediction: Serbia vs. Switzerland - June 21, 2018


The title – the end of mathematics – is exaggerated of course. It doesn’t mean that mathematics will vanish as a branch of science. The purpose of the title is to express a change in understanding the origin of mathematics. A bit like a paradigm shift.
It isn’t a new subject because the ancient Greek philosophers had already the opinion that mathematics is – in some way – the foundation of the universe (Pythagoreans). In 2007 Max Tegmark brought this idea back to live with his publication “The Mathematical Universe” (MUH).
The project “Beyond spacetime and quantum fields” describes a hypothesis about the mathematical structure of the universe. The hypothesis showed to be correct and this questions the theoretical structure of mathematics in relation to the “mathematical universe”. In other words, the posts are about the foundations of mathematics.
“The end of mathematics” is the original comprehensive website.
Next post: “”


Windows 10 calculator exe free
It\’s not even a percentage calculator. Windows area calculator calculator calculator for windows 7 fraction calculator. It has the essential math functions of addition, subtraction, multiplication, division, and percentage. Laws concerning the use of this software vary from country to country.
Windows 10 calculator exe free. Windows Apps for Calculators
Nov 16, · Hi, Thank you for your interest in Windows I suggest you to follow the suggestions below and check if that works for you: Open the Task manager. Here’s a tip: Press CTRL+Shift+ESC. Click File > Run New Task. Make sure you have a check mark beside “Create this task with administrative privileges”. Type CMD. Mar 07, · While Windows 10 users can take advantage of Microsoft Calculator app, a built-in tool with all essential and advanced features, those on Windows 8 don\’t get the same benefit. Calculator Free is one of the apps that seek to bridge that gap and provide you with a convenient desktop calculator. In that vein, this tool runs only on Windows.7/10(). Feb 26, · Calculator in Windows I can\’t locate replace.me file for the W10 calculator app. I want to send a desktop or taskbar icon out for quick access (as I did with W7) but no search locates it. Can someone direct me to the correct path? This thread is locked. You can follow the question or vote as helpful, but you cannot reply to this thread.
Download Calculator Free for Windows 10 for Windows – replace.me
The Calculator app for Windows 10 is a touch-friendly version перейти на страницу the desktop calculator in previous versions of Windows. You can open multiple calculators at the same time in resizable windows on the desktop and switch between Standard, Scientific, Programmer, Date calculation, and Converter modes.
To get started, select the Start button, and then select Calculator in the list of apps. Select the Open Navigation button to switch modes. Use Standard mode for basic math, Scientific for верстка microsoft office 2007 enterprise download for pc free download Вам calculations, Programmer for binary code, Date calculation for working with dates, and options under Converter for converting units of measurement.
The calculator can help you calculate datesconvert currencyand if you\’re using the Standard mode, you can cqlculator the calculator window on top of other windows. Open Calculator. Windows 10 More Need photoshop cs2 run on windows help?
Expand your skills. Get new features first. Was this information helpful? Calculstor No. Thank you! Any more feedback? The more you tell us the caldulator we can help. Can you help us improve? Resolved my issue. Clear instructions. Easy to follow. No jargon. Pictures helped. Windows 10 calculator exe free match my screen. Incorrect instructions. Too technical. Not enough information.
Not windows 10 calculator exe free pictures. Any additional feedback? Submit feedback. Thank you for calculato feedback!


Scatter diagram – 7QC Tools
Scatter diagram is a tool for analyzing relationships between two variables. In the two variables chosen one variable is plotted on the horizontal axis and the other variable is plotted on the vertical axis. The pattern of their intersecting points can graphically show the relationship patterns between the two variables.
Mostly the scatter diagram is used to prove or disprove cause-and-effect relationships between two variables which helps in decision making during the Problem Solving process.
To understand whether there is any relationship between the atmospheric temperature and the Ice cream sales figure, daily atmospheric temperature can be considered as one variable and the daily sales revenue can be considered as the second variable. These data can be plotted using a scatter diagram and the relationships can be inferred from it.
The above example indicates that there is a reasonable increase in the ice cream sales with respect to the daily temperature. The scatter Diagram indicates that the the trend of the sales is on increase with respect to temperature. This diagram proves that the there exist a relationship between the daily temperature and the ice cream sales which is also a positive correlation.
The relationship varies by the nature of the correlation. The various type of correlation that can possibly exist are detailed below.
When two variables are put into scatter diagram the obvious results fall into any of the above five correlations. These information helps us to take decisions during the problem solving process.
When we consider a machine shop, if there is a doubt that the coolant concentration affects the surface finish and needs some clarity if the relationship does really exists to take further decisions a Scatter Diagram can be used as a tool to prove or disprove the existence of the relationship. Here Coolant concentration and Roughness average becomes two variables and correlations can be verified.
Even when this is considered a important tool in arriving at decisions we must be very careful in choosing the variables to compare. If we take two variables such as TV Sales figure Vs Hand Bag sales Figure and want to know if there is any relationship between these two it is obviously going to be of no use from the correlation. Because the two variables does not infer with each other logically. Instead if there is a comparison to between the two variables such as TV Sales Figure Vs Stabilizer sales Figure the two variables has some logic to do so. Therefore it is important to carefully select the variables to have an effective results from the Scatter Diagram.
We believe the content posted above has helped you to learn the basic explanation about the Scatter Diagram which is one of the 7 QC tools used for problem solving. We would be glad to hear your comments in the comments section below.
Few books recommended to read on 7QC Tools are given below


- visit a college
- about us
Focus on basic mathematical concepts to calculate metric- apothecary conversion, dosage problems, intravenous flow rates using the ratio/proportion and dimensional analysis methods. These calculations will focus application to acute care, long-term care, and pediatric specialty areas. Prerequisites: Current student in Nursing program or permission of Department or Division.
|In Person||01/09/2017- 01/10/2017||M,Tu||5:00PM- 9:00PM||
3 of 20 Seats Available
|In Person||01/11/2017- 01/12/2017||W,Th||8:00AM- 12:00PM||
No Seats Available
SUN System The Shared Unique Number (SUN) System helps students identify courses that will directly transfer among Arizona's community colleges and three public universities. Using the SUN System, students can easily search for and enroll in courses that offer direct equivalency at other Arizona colleges and universities. SUN courses have their own unique course number and prefix listed alongside each college's course number.
Visit www.azsunsystem.com for more information.


Ruby Matrix, the Forgotten Library
This guest post is contributed by Matthew Kirk, who is a partner at Modulus 7, specializing in software development and strategy. The basis of his career has been around utilizing science to improve businesses. He has spoken at technology conferences around the world and in his spare time, he enjoys traveling and adding to his 2000+ vinyl record collection.
Remember matrices from math class? No not the movie, but the rectangular array of numbers. While you might not see it often, Ruby has a matrix implementation that is well tested and allows you to accomplish tough calculations quickly.
While I won’t be able to teach you everything there is to be known about matrices, we will cover how to use matrices within Ruby as well as some quirks and their major selling points. By the end of this I hope that you delve deeper into learning about matrices and use them in your next project.
What are matrices?
A matrix according to Wikipedia is a rectangular array of numbers. Used heavily in math, matrices are all over languages like R and Matlab. They can be a great way to store numerical data and simplify many difficult and tedious problems. Instead of solving systems of equations matrices can simplify these into one equation.
In terms of how Ruby implements matrices, Ruby stores all matrix rows into one big array. The only requirement is that the arrays are of the same dimension. So for each row that is added to a matrix each one must be of the same size.
Just like arrays, matrices are zero indexed meaning that the first row is index 0 and the first column is index 0. Unlike arrays though you have to have two indexes to get to an element:
Matrix library has some quirks. The
Matrix class allows non-numerical data to go into itself. This could be useful for storing things like symbols in a more x, y format but render most of the matrix functions useless.
Another quirk to be aware of:
Matrix[*rows] does not copy the rows objects but instead points to it. To avoid this use
Matrix.columns(columns). Implementation wise
Matrix[*rows] calls the function
Matrix.rows(rows, copy = false).
Iterating over matrices:
How do you iterate over a matrix? Most likely you would think that matrices read left to right top to bottom. And that’s true. But there are other cases as well.
In total there are 7 ways to iterate over a Matrix in ruby:
:allThis reads left to right top to bottom. This is the default case when you type
:diagonal: This only reads the diagonal elements or row index == column index
:off_diagonal: This will read everything not on the diagonal or row index != column index
:lower: This reads the lower triangle of the matrix or row index <= column index
:strict_lower: this is more strict and reads only row index < column index
:strict_upper: this is a strict upper triangle and is row index > column index
:upper: row index >= column index
Example: Parabola with matrix:
Imagine you want to fit a curve through three points. If you remember math class you might remember that you can do this by fitting a quadratic. For instance lets say we want a line that goes through (1,2) (3, 5.5) and (6, 6). To solve this we would write the equations:
The way to solve this would usually involve lots of algebra and substitutions. While it’s easy to solve this in the case where we already know the numbers it is difficult to come up with a general solution (try it I dare you).
Instead of worrying about solving this using non-matrix algebra we can solve it using matrix algebra. The first step is to rewrite the above system into this form:
To make it even easier to solve we would rewrite this as Ax = b. To solve this we would take the inverse of A and then multiply both sides by that. Which would yield:
Now that we know this, we can easily solve this using Ruby with the following formula.
While it’s close it won’t be correct unless you use
Rational. Ruby’s matrix library graciously utilizes functions that preserve precision. You would expect most libraries to convert to floats but ruby does not.
For instance you can change the above function call to:
Whenever possible try to preserve the precision!
The general case, fitting an n-power polynomial to n points:
Up above we only fit this curve to 3 points. But what about 4 or 15 points? This would be quite simple to do and would only require a little bit of modification:
While you might not use matrices every day, they can be useful to solve problems involving systems of equations. Ruby has a robust
matrix library that can be useful in finding solutions to these types of problems. Next time you want to fit a curve keep in mind matrices might be the best way to go!
For more information about matrices I recommend reading Wikipedia articles. There are lots of math professors who spend hours updating them tediously. If they are too confusing, think about picking up a book on matrix algebra like Matrix Computations.
Feel free to ask questions and give feedback in the comments section of this post. Thanks!


title: Overfitting Has Many Faces
Overfitting Has Many Faces
If a learning algorithm fits a given training set well, this does not simply indicate a good hypothesis. Overfitting occurs when the hypothesis function J(Θ) fits your training set too closely having a high variance and low error on the training set while having a high test error on any other data.
In other words, overfitting occrus if the error of the hypothesis as measured on the data set that was used to train the parameters happens to be lower than the error on any other data set.
Choosing an Optimal Polynomial Degree
Choosing the right degree of polynomial for the hypothesis function is important in avoiding overfitting. This can be achieved by testing each degree of polynomial and observing the effect on the error result over various parts of the data set. Hence, we can break down our data set into 3 parts that can be used in optimizing the hypothesis’ theta and polynomial degree.
A good break-down ratio of the data set is:
- Training set: 60%
- Cross validation: 20%
- Test set: 20%
The three error values can thus be calculatted by the following method:1
- Use the training set for each polynomial degree in order to optimize the parameters in
- Use the cross validation set to find the polynomial degree with the lowest error
- Use the test set to estimate the generalization error
Ways to Fix Overfitting
These are some of the ways to address overfitting:
- Getting more training examples
- Trying a smaller set of features
- Increasing the parameter


I spent the first day of summer (teacher summer, that is, not meteorological summer) having fun with math problems! I worked with other teachers and math coaches from our district to design low floor/high ceiling math explorations.
What is low floor/high ceiling you ask? It’s a math problem (or I suppose, any subject problem) that can be accessed at many levels. All students have a way in to the problem–kids that might struggle with the subject, all the way up to the experts. Nobody is left out of these challenges! Often, they are open-ended, inquiry-based, and/or student-driven. Check out Dan Meyer’s blog for some great examples, or YouCubed from Stanford based on the work of Jo Boaler, or these 3-act math problems geared towards elementary math standards. Fun, right?!
Teaching math using these types of explorations is a ton of fun, for teachers and students. Engagement is high, and all students are reminded that puzzling, and persevering, is rewarding. Even after we’ve moved on from the inquiry in the classroom, students will come up to me days and weeks later to tell me how they’ve continued to grapple with the ideas on their own–new approaches, or new solutions, or even new math questions to pursue.
Here’s a 3-act that I made a year ago, but haven’t yet used with students; it can be used for fractions, multiplication/division, money, or more! And here’s a quick prompt we made today; I have used a similar prompt with 4th grade students, with amazing returns! It wasn’t enough for them to figure out how many cans there were; we also figured out how much it would all cost, how many calories in the display, and how many fluid ounces of soda were in the display. TONS of multiplication!
What are your favorite resources for engaging low floor/high ceiling math problems? Please share! I’m going to keep my eyes open over the summer for pictures and videos I could take that would translate to math exploration in the classroom (or maybe…literacy prompts? Writing? What would low floor/high ceiling look like in those subjects? Let’s try it!).


Section One; Random Numbers
The use of random numbers in simulations has become an essential tool in various fields such as engineering, physics, economics, and computer science. Random numbers help generate random events, allowing simulations to model complex scenarios that cannot be replicated in real life. In this essay, I will discuss the applications of random numbers in simulations and their benefits.
Random numbers are a key component of Monte Carlo simulations, a technique used to model complex scenarios and estimate probabilities in a wide range of fields. Monte Carlo simulations use random numbers to generate a large number of possible outcomes, which can be used to estimate the likelihood of different scenarios and analyze risk.
A flip of a coin is a good first look at random, the result of the toss is either a head or tail. In a 'fair' coin the chance should be equal. For ease of programming we will assign 0 to a head and 1 to a tail.
Much of the computing in Python is done in computer programs that have been written and placed in packages. These generally make the computer code more readable and also allow powerful tools that don't need to be rewritten. So first we will import some useful packages
In the previous cell the toss() function was executed ten times with print statements and then 1,000 times.
In the next example we will use the tossing of dice to explore the nature of random numbers. If you execute the previous cell, you will generally get different answers each time you run it. That will be shown in the following examples. The Python code may look more complicated but the only new item is the list denoted by brackets [ ] . Instead of just adding up the number of each, we can store the individual results in a list. That will be explained in the computer code.
Monte Carlo simulation is a computational technique that utilizes random numbers to simulate a wide range of processes and systems. The method derives its name from the renowned Monte Carlo Casino, known for its games of chance and unpredictability. The core idea behind Monte Carlo simulation is to repeatedly sample random values for uncertain variables within a model, allowing us to estimate the behavior and outcomes of the system.
In the next few examples we will look at the impact of using more sets of data in creating random number simulations. The first example uses 5 sets of the 10 rolls. The num_simulations = 5 and num_roll = 10 as defined in the previous cell
There you see the results of the two dice, each roll for each set and then each of the five sets are plotted separately. The only real information here is a visualization of the randomness of each roll.
Here we would expect a Gaussian or Normal curve: this will look better as we increase the number of sets.
Next we will increase the number of sets from 5 to 30


Psychologist Researcher at the Mathematical Modeling Center of the Faculty of Physical and Mathematical Sciences of the University of Chile
Psychologist, master’s degree in educational psychology from the Catholic University of Chile and doctorate in education from the University of Manchester in the United Kingdom. Her research has focused on understanding teaching processes in the area of mathematics education and the use of this knowledge for the development of learning resources, design of evaluation models and measurement instruments. She is currently a researcher at the Mathematical Modeling Center of the Faculty of Physical and Mathematical Sciences of the University of Chile. Her areas of research are the relationship of gender and mathematics in school age and the processes that explain why women choose and persist in academic careers with high mathematical content. In particular, she is interested in understanding the contextual and institutional difficulties that women of different ages must face in order to develop positive relationships with mathematics, for which she uses sociocultural theoretical models and mixed research methodologies.


3 edition of Modern mathematics for schools;♭in 9 books!. found in the catalog.
Modern mathematics for schools;♭in 9 books!.
Scottish Mathematics Group.
1969 by Blackie; Chambers .
Written in English
|The Physical Object|
|Number of Pages||285|
SPMG Topics and Acitivities Bk. 2: Math by Scottish Primary Mathematics Group and a great selection of related books, art and collectibles available now at Most of our books are of a technical nature, i.e. Mathematics, Chemistry, Physics, Medical, Electronics, and over other fields. We do have some fiction and non-fiction that we are adding to all the time. Currently we have o books listed and have approximately another , yet to inventory and list. NOTE! INTERNATIONAL BUYERS! Unlike static PDF Student Resource Guide For Excursions In Modern Mathematics 8th Edition solution manuals or printed answer keys, our experts show you how to solve each problem step-by-step. No need to wait for office hours or assignments to be graded to find out where you took a wrong turn. PDF New General Mathematics 2 with answers: Bk. 2 Download I am looking to PDF New General Mathematics 2 with answers: Bk. 2 Download book in format PDF, Ebook, ePub, Kindle or mobi. so that i can read directly on the device I have. through browsing the internet I tried to find the New General Mathematics 2 with answers: Bk. 2 PDF Online book in the format, many sites.
Federal-Provincial Conference of First Ministers, Ottawa, September 16, 1970.
romance of nickel
Testimony of mariners
The kingdom of this world
Back to School Review, With Pencil (Back to School Review)
Answer to John Robinson of Leyden by a Puritan Friend (Harvard Theological Studies : Volume 9)
Tetleys Brewery Wharf
Lead oxides: chemistry, technology, battery manufacturing uses, history
Lethal diseases of the ascending aorta
Transcarpathia--bridgehead Or Periphery
Research in organizational change and development.
police and change
Modern Mathematics for Schools Book 9 Hardcover – Import, January 1, by Scottish Mathematics Group (Author) See all formats and editions Hide other formats and editionsAuthor: Scottish Mathematics Group. Modern Mathematics for Schools book.
Read reviews from world’s largest community for readers. Goodreads helps you keep track of books you want to read. Start by marking “Modern Mathematics for Schools: Bk.
1” as Want to Read: Want to Read saving 2/5(1). Modern School Mathematics Algebra 1 [Mary P. Dolciani, William Wooton, Edwin F. Beckenbach, Ray C. Jurgensen, Alfred J. Donnelly] on *FREE* shipping on qualifying offers. Modern School Mathematics Algebra 15/5(2). Textbook solutions for Excursions in Modern Mathematics (9th Edition) 9th Edition Peter Tannenbaum and others in this series.
View step-by-step homework solutions for your homework. Ask our subject experts for help answering any of your homework questions. Purchase Introduction to Modern Mathematics - 1st Edition. Print Book & E-Book. ISBNBook Edition: 1.
The books introduced “Modern Mathematics” topics such as Set theory, Matrices, Vectors and Mappings alongside the more traditional topics. An innovative feature of the course is the series of Computer topics which appeared from book 4 onwards. The Modern mathematics for schools;♭in 9 books!.
book was that these would form an introduction to computer studies. Download Excursions in Modern Mathematics 9th Edition Tannenbaum book pdf free download link or read online here in PDF.
Read online Excursions in Modern Mathematics 9th Edition Tannenbaum book pdf free download link book now. All books are in clear copy here, and all files are secure so don't worry about it.
B&N Exclusives Baby Boutique Boxed Sets Graphic Novels for Young Readers Kids' Classics Kids' Book Awards Personalized Books STEAM/STEM Books & Toys Trend Shop Top Young Reader Series Age Groups 0 - 2 Years 3 - 5 Years 6 - 8 Years 9 - 12 Years. This book is intended Modern mathematics for schools;♭in 9 books!.
book be used by children ages 5 to 6. Other age groups will also benefit from the book. Anyone can use this book globally, although the curriculum may differ slightly from one region to the other. This is so because the core content of Mathematics is the same around the world.
College Book Bundle [Mathematics in the Modern World and Fundamentals of Management] PHP College Book for sale for Marketing Students 📖 php for 2 +sf thru JRS📖 Meet ups: Dau, Mabalacat Pampanga+20php HF Holy Angel University, Angeles City, Pampanga+40php HF Book title: •Fundamentals of Management Eight Edition by Ricky Griffin Condition: GC, with highlights 💰Price:.
REX Book Store Inc. REX Knowledge Center, Sen M Cuenco Sr, Quezon City, Metro Manila, PH (02) We have solutions for your book. Chapter: CH1 CH2 CH3 CH4 CH5 CH6 CH7 CH8 CH9 CH10 CH11 CH12 CH13 CH14 CH15 CH16 CH17 Problem: 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E 19E 20E 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E 31E 32E 33E 34E 35E 36E 37E 38E 39E 40E 41E 42E 43E 44E 45E 46E 47E 48E 49E 50E 51E 52E 53E 54E 55E 56E 57E.
Get cozy and expand your home library with a large online selection of books at Fast & Free shipping on many items. Connected Mathematics 2 Grade 7 Student Edition Textbook and Teacher Resources.
$ Free shipping. Modern Algebra Structure And Method Book 1, Dolicini Berman Freilich $ $ shipping. - Buy Modern School Mathematics: Book 3 (Rev. Edn.) book online at best prices in India on Read Modern School Mathematics: Book 3 (Rev.
Edn.) book reviews & author details and more at Free delivery on qualified : B. Choudhari. Concepts of Modern Mathematics - Ebook written by Ian Stewart.
Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Concepts of Modern Mathematics.
Great deals on High School Math Textbooks & Educational Books Get cozy and expand your home library with a large online selection of books at Fast & Free shipping on many items.
Publisher Summary. This chapter focuses on the algebra of sets. The concept of set is one of the fundamental concepts of mathematics.
The branch of mathematics concerned with the study of the general properties of sets, regardless of the nature of the objects that form those sets, is known as set theory and is regarded as the foundation of modern mathematics.
Book The architecture of modern mathematics essays in history and philosophy pdf Book The architecture of modern mathematics essays in history and philosophy pdf Pages By J. Ferreirós, J. Gray Publisher: Oxford University Press, Year: ISBN:Search in Description: This edited.
Modern Publishers publishes CBSE curriculum-based text books for mainly higher classes(10th,12th,UG & PG).It publishes lots of books such as modern books, modern abc of biology, modern abc of chemistry, modern abc of mathematics.
Modern Mathematics for Schools book. Read reviews from world’s largest community for readers.4/5(1). These notes, together with the book The Heart of Mathematics [HM] by Burger and Starbird, are the texts for the ANU College Mathematics Minor for Years 11 and 12 students.
If you are doing this course you will have a strong interest in mathematics, and probably be in the top 5% or so of students academically. What is Mathematics. Excursions in Modern Mathematics (Looseleaf) Expertly curated help for Excursions in Modern Mathematics (Looseleaf).
Plus easy-to-understand solutions written by experts for thousands of other textbooks. *You will get your 1st month of Bartleby for FREE when you bundle with these textbooks where solutions are available ($ if sold separately.). Excursions in Modern Mathematics, Books a la carte edition (9th Edition) Excursions in Modern Mathematics, Books a la carte edition (9th Edition) Solutions Manual is an interesting book.
My concepts were clear after reading this book. All fundamentals are deeply explained with examples. The modern mathematics series by Edwina Deans,American Book Co. edition, in English. Beta Mathematics old school maths books. Sadly this series is now out of print, but here is a list with the book details to get you started on your search for secondhand copies.
History of Modern Mathematics Cornell University Library historical math monographs Issue 1 of Mathematical monographs Issue 1 of Mathematical monographs, ed. by Mansfield Meriman and R.S.
Woodward Issue 1 of Translations of mathematical monographs: Author: David Eugene Smith: Edition: 4, reprint: Publisher: J. Wiley & Sons, Original from. ELEMENTARY SCHOOL MATHEMATICS - NEW DIRECTIONS by Deans, Edwina and a great selection of related books, art and collectibles available now at The Modern Mathematics Series: Meeting Mathematics, Teacher's Edition, Annotated and Keyed and the copy can include previous owner inscriptions.
An ex-library book and may have standard library. The foundations of mathematics involves the axiomatic method. This means that in mathematics, one writes down axioms and proves theorems from the axioms.
The justi-ﬁcation for the axioms (why they are interesting, or true in some sense, or worth studying) is part of the motivation, or physics, or philosophy, not part of the mathematics. The. The Global Profiles series gets underway with this engaging introduction to some ideas in modern mathematics by way of 13 biographies, covering Charles Babbage and Ada Lovelace, George Boole, Georg Cantor, Sophia Kovalevsky, Srinivasa Ramanujan, Emmy Noether, Shiing-Shen Chern, Alan Turing, Stanislaw Ulam, Benoit Mandelbrot, Julia Bowman Robinson, and John Conway.
Almost all of. Since modern mathematics textbooks were introduced in the late 19th century Korea, arithmetic experts started to teach modern mathematics using Arabic numerals at village schools and churches.
sample textbooks for grade 7 and a book of experimental units for grade 8. In the school yearthese seventh and eighth grade books were used by about teachers in many parts of the country,and then further revised in the summer of Mathematice is fascinating to.
ways in which mathematics is used and communicated. We gain such an understanding through the study of ethnomathematics. Ethnomathematics encourages us to witness and struggle to understand how mathematics continues to be culturally adapted and used by people around the planet and throughout time.
Traditionally in mathematics classrooms. For example, x 2 + 14 = x + 5 is reduced to x 2 + 9 = x. The above discussion uses modern mathematical notation for the types of problems that the book discusses.
However, in al-Khwārizmī's day, most of this notation had not yet been invented, so he had to use ordinary text to present problems and their solutions. For example, for one problem. Facts is your complete guide to Excursions in Modern Mathematics. In this book, you will learn topics such as as those in your book plus much more.
With key features such as key terms, people and places, Facts gives you all the information you need to prepare for your next exam. ThriftBooks sells millions of used books at the lowest everyday prices. We personally assess every book's quality and offer rare, out-of-print treasures.
We deliver the joy of reading in % recyclable packaging with free standard shipping on US orders over $ This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers students at both high school and college levels an excellent mathematics workbook.
Filled with rigorous problems, it assists students in developing and cultivating their logic and probability skills. edition. Discrete Mathematics provides an introduction to some of the fundamental concepts in modern mathematics.
Abundant examples help explain the principles and practices of discrete mathematics. The book intends to cover material required by readers for whom mathematics is just a tool, as well as provide a strong foundation for mathematics majors.
Modern Mathematics for Schools: Pupils' Book Bk. 9 Nelson Thornes Ltd, Spiral-bound, ; Modern Mathematics for Schools: Pupils' Book Bk. 8 Nelson Thornes Ltd, Paperback, ; Modern Mathematics for Schools Bk 2 Pb Chambers Harrap Publishers Ltd, Paperback, ; Modern Mathematics for Schools Bk 3 Pb Chambers Harrap Publishers Ltd.
About The Book. For courses in Liberal Arts Mathematics. Math: Applicable, Accessible, Modern Excursions in Modern Mathematics introduces readers to the Read more. FINDING THE BEST PRICES Most of the same websites that sell books to students are also interested in buying books.
We provide a list of quotes below. Excursions in Modern Mathematics, Books a la Carte Edition introduces readers to the power and beauty of math. By developing an appreciation for the aesthetics and applicability of mathematics, readers who previously felt math was an “unknowable” subject can approach it with a new perspective.
A Student's Guide to the Study, Practice, and Tools of Modern Mathematics provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use various mathematical tools, from LaTeX and Beamer to Mathematica and Maple to MATLAB and R.
Along with a color insert, the text include.ThriftBooks sells millions of used books at the lowest everyday prices.
We personally assess every book's quality and offer rare, out-of-print treasures. We deliver the joy of reading in % recyclable packaging with free standard shipping on US orders over $b) Using the second method, we place between and -4 approximating the location.
Practice 10 a) Plot on the number line with a black dot. b) Plot with a green dot. Solution: Click here to check your answer. Often in real life we desire to know which is a larger amount.
If there are 2 piles of cash on a table most people would.


The Blue and Purple Sudoku for Kids Worksheet is a great way to introduce young children to the world of Sudoku.
It is designed to help kids learn the basics of the game while having fun. The worksheet has nine 3×3 boxes, each of which is filled with blue or purple numbers.
The aim of the game is to fill in the empty cells with numbers that do not appear in the same row, column, or 3×3 box.
The worksheet also features helpful hints and tips to help kids understand how to fill in the cells correctly. With a colorful design and easy instructions, this worksheet is the perfect way to get kids interested in Sudoku!


During this A Level Further Maths course, you’ll take your mathematical knowledge to the next level and develop your understanding in areas such as algebra, hyperbolic functions, vectors, linear programming, centres of mass, and dimension analysis.
Depending on the degree and career path you hope to pursue, we recommend that you study A Levels in the following subjects alongside this course: A Level Physics, A Level Economics, A Level Chemistry, and A Level Geography.
DEGREES THIS SUBJECT COULD LEAD TO
Students studying A Level Further Maths have a variety of degrees to choose from once they have successfully completed their course, including degrees in maths, engineering, sciences, geography and computer science.
FUTURE CAREER OPTIONS
You’ll gain skills relevant to future careers in areas such as:
Fully prepared for A Level Further Maths qualification from AQA.
We recommend that you have at least a grade 4/C in GCSE Maths.
Three written exams.
In order to enrol in the course, please contact us.


In the late nineteenth century the mathematician George Cantor dedicated his studies to the mathematical concepts of the infinite.
Thus, after Cantor, there can be no argument about the central place of the infinite in mathematics… Yet despite all the evidence, many modern mathematicians persist in denying the objectivity of infinity. (p358)
How can this perversity of modern mathematics be resolved? Why, if there was to be no argument about the objective existence of infinity, did argument persist “despite all the evidence”? And what evidence? The answer is to be found in discovering what Cantor actually showed. Cantor says that the infinite arises:
First when it is realised in the most complete form, in a fully independent other-worldly being, in Deo [in god] where I call it the Absolute… second when it occurs in the contingent, created world; third… as a mathematical magnitude…
I wish to make a sharp contrast between the Absolute and the transfinite, that is the actual infinities of the last two sorts, which are clearly limited, subject to further increase, and thus related to the finite. (Quoted by Barrow, The Infinite Book, p94)
In Cantor’s mathematics, only infinity in god coincides with Woods’ idea of the objectivity of infinity – an objectively existing infinite god. And indeed there was “no argument” about it.


Australian Algebra Conference
Saturday November 30 - Sunday December 01, 2019
Venue: RMIT University, Melbourne
The aim of the annual Australian Algebra Conference is to foster communication between algebraists in Australia. We interpret algebra broadly, including areas such as topological algebra, algebraic logic, graph theory and coding theory. The conference is run by the Australian Algebra Group, which is a special interest group of the Australian Mathematical Society.
About the venue
RMIT Building 8, Bowen St, Melbourne
Room 08-04-13 ("Mega Flex 3")
Getting to RMIT
RMIT is conveniently located very close to Melbourne Central station, and quite near to Chinatown. See the map above for directions to the conference venue.
The dinner will be held at 6 o'clock on Saturday evening 30/11/2019 at the Oxford Scholar Hotel, on the corner of Swanston St and a'Beckett St, Melbourne. See below for the menu.
The invited speaker is Professor Ales Drapal from Charles University in Prague, Czech Republic.
The conference booklet will be available closer to the event.
The list of talk titles will appear here later.
Gordon Preston Prize
The Gordon Preston Prize is awarded for the best presentation at the AAC given by a current student based at an Australian or overseas university. The presentations will be judged by a panel appointed by the executive committee. The winner of the prize will receive $300. The Rules for the Gordon Preston Prize are available on the website of the Australian Algebra Group.
Try travel booking websites like Wotif, Expedia, Agoda, Booking (.com.au) for deals.
- Graham Clarke, RMIT --- Email: firstname.lastname@example.org
- Joanne Hall, RMIT --- Email: email@example.com
- Asha Rao, RMIT --- Email: firstname.lastname@example.org
- Lawrence Reeves, University of Melbourne --- Email: email@example.com
- Marcel Jackson, Latrobe University --- Email: firstname.lastname@example.org
- Tomasz Kowalski, Latrobe University --- Email: T.Kowalski@latrobe.edu.au
- Brian Davey, Latrobe University --- Email: B.Davey@latrobe.edu.au
Registration and Payment
To register, go here: https://register.austms.org.au/
(Registration is now closed.)
- Members of the Australian Algebra Group: free
- Students: free
- Members of the AustMS who are not members of the Australian Algebra Group: $30 (by bank transfer)
- Non-members of the AustMS: $40 (by bank transfer)
- Non-students: $40
- Students: $20
The conference series particularly encourages graduate students to give presentations on their work. Students from Australian universities, regardless of their intention to give a talk, are entitled to apply for a travel contribution. The amount will be a function of the number of applicants and where you are coming from, and will be announced soon after the application deadline (pending). Preference will be given to students coming from outside the Melbourne metropolitan area. Unfortunately, it is not possible to provide any contribution to costs for students from non-Australian universities. Retired or unwaged participants may also request support by emailing the local organisers directly.


Hi everyone! I’m back with another webcam project, as usual. :) I’ve been having a lot of fun making cool things using my webcam over the last couple of months. This time, I’ve created an obstacle detector which uses a cheap laser pointer and a webcam to determine how far an object is from the camera. I worked with my cousins, Anuj Karpatne and Prateek Raj on this project.
So, here’s how it works. A laser pointer is fixed below the camera at a known distance (as you can see in the picture above). The pointer is kept parallel to the optical axis of the camera. Then, a laser-beam is projected on an obstacle which is supposedly in the camera’s field of vision. The scene, along with laser dot is captured by the camera. Then, the image is scanned for the brightest pixels (we are assuming that the laser dot is the brightest point in the scene). Then, we calculate how far along the y-axis the laser dot is from the center of the image. The farther from the center, the closer we are to the obstacle. So, the distance from the object (D) is inversely proportional to the number of pixels from the center of the image (y):
D = hY/2y * cot (A/2)
Where the constants used are:
h = the actual distance between the laser pointer and the optical axis of the camera.
Y = total number of pixels along the y-axis
A = angle of view of the camera
D α 1/y
Or, D = k/y (where k is the proportionality constant for all the constants used above)
We used an experimental approach to determine the value of k. We wrote a simple program in C# to do the entire image processing work and for finding the position of the laser dot in the scene. We calibrated the apparatus by placing an obstacle at known distances from the center of the camera and noting down the number of pixels the laser dot is from the center of the image along the y-axis. After taking several readings, we obtained the value of k. By using this value, we were actually able to determine how far an obstacle is, from the camera.
Well, we had a lot of fun working on this project! I hope you find it interesting. I’d love to hear your comments and ideas. :)


Complex natural systems defy standard mathematical analysis, so one ecologist is throwing out the equations.
Sometimes ecological data just don’t make sense. The sockeye salmon that spawn in British Columbia’s Fraser River offer a prime example. Scientists have tracked the fishery there since 1948, through numerous upswings and downswings. At first, population numbers seemed inversely correlated with ocean temperatures: The northern Pacific Ocean surface warms and then cools again every few decades, and in the early years of tracking, fish numbers seemed to rise when sea surface temperature fell. To biologists this seemed reasonable, since salmon thrive in cold waters. Represented as an equation, the population-temperature relationship also gave fishery managers a basis for setting catch limits so the salmon population did not crash.
But in the mid-1970s something strange happened: Ocean temperatures and fish numbers went out of sync. The tight correlation that scientists thought they had found between the two variables now seemed illusory, and the salmon population appeared to fluctuate randomly.
Trying to manage a major fishery with such a primitive understanding of its biology seems like folly to George Sugihara, an ecologist at the Scripps Institution of Oceanography in San Diego. But he and his colleagues now think they have solved the mystery of the Fraser River salmon. Their crucial insight? Throw out the equations.
Sugihara’s team has developed an approach based on chaos theory that they call “empirical dynamic modeling,” which makes no assumptions about salmon biology and uses only raw data as input. In designing it, the scientists found that sea surface temperature can in fact help predict population fluctuations, even though the two are not correlated in a simple way. Empirical dynamic modeling, Sugihara said, can reveal hidden causal relationships that lurk in the complex systems that abound in nature.
Sugihara and his colleagues are now putting their insight to use. Earlier this year they reported in the Proceedings of the National Academy of Sciences (PNAS) that their method predicted the 2014 Fraser River salmon run more precisely than any other method. Sugihara’s technique predicted a run of between 4.5 million and 9.1 million fish, while the Pacific Salmon Commission’s models predicted anywhere from 6.9 million to 20 million fish — a forecast so broad as to be of little benefit to, for instance, a fisher wanting to know how many boats to deploy in the coming season. The final count was around 8.8 million.
This success built on an earlier result Sugihara and his colleagues had achieved with Pacific sardines, and they’re working with scientists at the National Oceanographic and Atmospheric Administration (NOAA) to apply the methods to Gulf and Atlantic menhaden. Leading ecologists hope Sugihara’s methods can provide the field with some much-needed predictive power, and not just for marine fisheries but for many other ecosystems. Don DeAngelis, an ecologist with the U.S. Geological Survey in Miami, calls it “a huge theoretical breakthrough.”
Sugihara and others are now starting to apply his methods not just in ecology but in finance, neuroscience and even genetics. These fields all involve complex, constantly changing phenomena that are difficult or impossible to predict using the equation-based models that have dominated science for the past 300 years. For such systems, DeAngelis said, empirical dynamic modeling “may very well be the future.”
A New Set of Coordinates
The roots of empirical dynamic modeling go back more than 30 years. In the late 1970s, the Dutch mathematician Floris Takens was studying chaos theory, which had begun to emerge in the 1960s as scientists recognized that many of nature’s complex phenomena seem to defy prediction. In chaotic systems, small perturbations can have large and seemingly unpredictable effects, as in the archetypical example of a butterfly’s flapping wings influencing the weather thousands of miles away.
Takens helped find order in the chaos. Along with the physicist David Ruelle, he developed the notion of a “strange attractor” — a set of points in a coordinate system made of the variables that influence a system, around which the system’s state, plotted over time, swirls like a ball of yarn.
In many natural systems, however, the number of relevant variables that make up the coordinate system is immense. The factors that determine the weather in a certain place at a certain time are almost limitless, and some of these can be very hard to measure — the air pressure three miles above the North Pole, for example.
But let’s say you could consistently and accurately measure one variable, such as the temperature in New York City. Takens found a way to use present and past measurements of that one variable to capture all the information in the system. The method involves creating an alternate coordinate system from those past measurements; in other words, one coordinate axis might be the temperature in Times Square today, a second axis might be the temperature yesterday, a third the temperature two days ago, and so on. Takens showed that the full state of a chaotic system can, in theory at least, be embedded in a time series of a single variable. He published his “embedding theorem” in 1981.
The theorem “caused a big hullabaloo,” said Timothy Sauer, a mathematician at George Mason University in Fairfax, Va., who has extended the original theorem so it can be applied more generally.
The next step was for people to use it in the real world, but the messiness of nature had a way of impinging on the purity of Takens’ math. Despite the fact that weather provided much of the initial impetus for chaos theory, it rebuffed efforts at prediction, because too many constantly changing factors are involved, and no one variable can truly capture them all. Sauer said that Takens’ theorem can be most effectively applied to systems in which the number of influencing factors is relatively small.
Sugihara learned about Takens’ theorem as a Princeton graduate student working with Robert May, a physicist by training who switched to ecology in the early 1970s. May specialized in simple and elegant theoretical studies, including one proving that the population of even a single species could fluctuate chaotically. Sugihara became interested in seeing if he could build on May’s advances using real-world data. In 1986, a few years after earning his doctorate, Sugihara moved to Scripps to get his hands on plankton data that a researcher there had collected in the 1920s and ’30s. “It’s an amazing data set,” Sugihara said. “I knew there was some way to get good information out of it.”
Based on the plankton data as well as work on measles and chicken-pox cases by other researchers, Sugihara and May published a paper in Nature in 1990 showing how Takens’ theorem could help make short-term predictions of some nonlinear systems. The essence of the method involves identifying points in a system’s attractor graph that are close to the point representing the system’s present state. For one or two time steps, one can then predict that the system will evolve similarly to how it did in the past. The paper has since been cited more than 1,000 times by scientists all over the disciplinary map. The paper also prompted Sugihara to make a mid-career foray into finance, as firms were very interested in forecasting stock prices using methods similar to those he had applied in ecology.
In 2002, Sugihara returned to science. He had unfinished business: convincing the world that ecosystems, though complex and chaotic, could be predicted, and that managers could use those predictions to do their jobs better. “I feel like I have a mission,” he said, “to get people to understand how this all works — to begin to embrace natural systems as they are as opposed to as we hope they would be.”


Project Euler – Math Programming Projects
Oh you math teachers are going to love this one. No, really you will. And honestly it may encourage some of your programming students who don’t think they like math to get interested. I’m talking about a web site called Project Euler. There are well over 200 mathematical puzzles listed here that are best solved with the aid of a computer program. You probably could do them with pencil and paper but you could also probably build a large building without power tools. But do you want to?
From the about page on the Project Euler website:
What is Project Euler?
Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.
The motivation for starting Project Euler, and its continuation, is to provide a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context.
Have some students you want to challenge? Or perhaps want to challenge yourself? These may be just the projects you are looking for. Also as I understand it there is a ranking system for registered members so yet anotter chance for students to compete and measure themselves against each other if they are so inclined.
Hat tip to Megan Golding on whose blog I found this link. She’s using these projects with middle school students so there is a large range of complexity here.
Published Wednesday, January 07, 2009 5:38 AM by Alfred Thompson


We hope you have found out all you need to know about Wren Academy and we look forward to receiving your application for a place in our Sixth Form.
The focus of our Sixth Form is on the study of A Levels which allow our students the best opportunity to progress into university and follow professional careers. We offer a range of courses in the Sixth Form. Our entrance requirements are as follows:
A Level: For September 2024, entry requirements we will be using an average points system, with a requirement of at least 5.5 in a students best 8 GCSEs.
For example, assume a student has these following GCSEs:
English Language 7
English Literature 5
This student has nine GCSEs; their best eight GCSEs would therefore not count their 4 in Business. An average point score of their best eight GCSEs would therefore be 50 points divided by 8 GCSEs giving an average of 6.25. As we are looking for an average points score of 5.5 this student would meet the requirements for Sixth Form entry.
There are also requirements to study particular subjects:
- A Grade 7 at GCSE Mathematics is needed for students to study Mathematics at A Level. Students who wish to study Further Mathematics can only do so with a Grade 8 in Mathematics at GCSE.
- A Grade 7 at GCSE Science is needed for students to study Science at A Level. Students will also require a Mathematics Grade 7 to study Biology, Chemistry or Physics at A Level.
- For all other subjects a Level 6 at GCSE is needed to take that same subject at A Level.


Distinguished Speaker Series
|February 4, 2022
Zoom info will follow soon
Herbert S. Winokur, Jr. Professor of Engineering and Applied Sciences, Faculty Director of the Institute for Applied Computational Science (IACS) and Department Chair of Applied Mathematics at Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS)
Learning Algorithms and Complex systems: Alloys
Over the last last thirty years we have experienced more than a billion-fold increase in hardware capabilities and a dizzying pace of acquiring and transmitting massive amounts of data. Learning algorithms have been the beneficiaries of these advances and today they are increasingly embedded in technologies that touch every aspect of humanity. However along with the abundance of promise there is an ever increasing amount of hype, in particular regarding the capabilities of learning algorithms to model, predict and control complex physical systems.
In this talk I would offer a perspective on forming alloys of learning algorithms and simulations for the prediction and control of complex systems. I will present novel algorithms and a comparative study of back-propagation algorithms for the modeling of chaotic dynamical systems, a fusion of reinforcement learning and scientific computing for modeling and control of complex flow-structure interactions. I will juxtapose successes and failures and argue that the proper fusion of domain knowledge and machine learning expertise are essential to advance human knowledge.