Homework two at Udacity’s CS101 gave a little shock to more than a student. The third loop of question 5 was:
n = any positive integer while n != 1: if n % 2 == 0: # the % means remainder, so this tests if n is even n = n / 2 else: n = 3 * n + 1
And the question was: will this loop end sooner or later, will it loop forever, or doesn’t anybody know?
To the abashment of many a student, the answer is “nobody knows”. Many people have tried running the loop with different values of n, you could even try to run it with the largest integer that your programming language and your hardware allow, and the loop always end, so why isn’t the correct answer “yes it ends”? This is a very good introduction to the concept of conjecture. According to the definition of the Merriam-Webster’s dictionary, a conjecture is:
2.c : a proposition (as in mathematics) before it has been proved or disproved
So here is the tricky part: no matter how hard anyone has tried, it has worked, but nobody has yet find a mathematical proof that that loop will end. This very simple little problem even has a proper, famous mathematical name, it’s the Collatz conjecture. If you search the web, you can find much about it. Very interesting is the Wolfram MathWorld’s page on the Collatz Problem: if you look on the right sidebar, you can find links to demo projects on this little tricky conjecture.
Some may argue that this all has little to do with CS101, learning about programming, but I think it was indeed quite appropriate: a high-level course should not only give you standard information on the subject, but it should also open your mind to new ideas, give you new paths to explore, expand your knowledge. I think that the students that were already familiar with the idea of a mathematical conjecture were immediately hinted by the “Unknown, to anyone” formulation of the third option, and even if they didn’t know of this specific problem, they might have started searching the web for something like “3n +1″. Google it and the problem shows up at the very top. Other students, who might have never heard of what a conjecture is, now have an idea, so I think that, even if it wasn’t something dealt with in the lectures, it is still a great way of teaching, because it asked students to actively look for something. Again, kudos Udacity!
A word to the wise: like so many other open problems in mathermatics, this conjecture is very easy to state, but it doesn’t mean it will be easy to prove, so you’d better think twice before you dive in and try to solve it!


Mathematics is one of the most important subjects in universities. It is a subject that requires logic, reasoning, and critical thinking. However, many students struggle with this subject, and it is not uncommon for them to feel intimidated and overwhelmed. In this article, we will look at some unique ways to ace your math exam and overcome your fear of this subject.
Understand the Basics
The first step in acing your math exam is to understand the basics. Mathematics is a subject that is built upon a foundation of concepts and principles. If you do not have a solid understanding of the basics, you will struggle with the more advanced topics. Make sure you have a good grasp of the fundamental concepts before moving on to more complex topics.
Practice, Practice, Practice
Practice is essential when it comes to mathematics. You cannot simply read a textbook or listen to a lecture and expect to understand the subject. You need to practice solving problems to develop your skills. The more you practice, the more you will become familiar with the subject, and the easier it will become for you.
Use Online Resources
There are many online resources available that can help you with your math exam. There are websites with practice problems, videos, and tutorials. Take advantage of these resources as they can be a valuable tool in your studies.
Get a Tutor
If you are struggling with mathematics, consider getting a tutor. A tutor can work with you one-on-one and help you understand the subject better. They can also provide you with personalized feedback and guidance, which can be invaluable when it comes to acing your math exam.
Ask for Help
Do not be afraid to ask for help. If you are struggling with a topic, ask your professor or classmates for help. Many universities have tutoring centers or study groups that can provide you with additional support. Do not let pride get in the way of your success.
One of the keys to acing your math exam is to stay organized. Keep your notes, textbooks, and study materials in order. Create a study schedule and stick to it. By staying organized, you will be able to focus on your studies and avoid distractions.
It is important to take breaks when studying for your math exam. Studying for long periods without a break can lead to burnout and decreased productivity. Take short breaks every hour or so to rest your mind and recharge.
Focus on Understanding, Not Memorization
One of the biggest mistakes students make when studying for their math exam is to focus on memorization. Math is not a subject that can be memorized. Instead, focus on understanding the concepts and principles. Once you understand the material, you will be able to apply it to different situations and solve problems more efficiently.
Finally, it is important to stay positive when studying for your math exam. A positive attitude can go a long way in helping you overcome your fear of the subject. Believe in yourself and your abilities. With hard work and dedication, you can ace your math exam.
In conclusion, mathematics is a subject that requires hard work, dedication, and practice. By following these tips and strategies, you can overcome your fear of the subject and ace your math exam. Remember to stay organized, stay positive, and most importantly, never give up.


While Maryland's Education Department is quick to tout the state's latest educational achievements, we're not so likely to hear about our failings. Here is a little secret: Maryland's math achievement is flagging. Maryland is one of the richest states - it has the highest median household income, according to a 2006 Census Bureau report. How come we're not at the top of the pack in math?
Friday, May 30, 2008
Op-Ed on Math in MD by Bob Embry
On May 29, 2008 The Baltimore Sun published an Op-Ed on Maryland's math problem that was written by Bob Embry, president of the Abell Foundation. Mr. Embry attended the K-12 Math Education Forum and quotes Professor Bill Schmidt, one of the panelists, in the article. This is great news for our chances of making progress on this issue in Maryland. Below is an excerpt from the Op-Ed:


A recent ScienceDaily article discusses implications of new research appearing in the Journal for Research in Mathematics Education, “Non-Traditional Mathematics Curriculum Results in Higher Standardized Test Scores.”
According to the article:
James Tarr, a professor in the MU College of Education, and Doug Grouws, a professor emeritus from MU, studied more than 3,000 high school students around the country to determine whether there is a difference in achievement when students study from an integrated mathematics program or a more traditional curriculum. Integrated mathematics is a curriculum that combines several mathematic topics, such as algebra, geometry and statistics, into single courses. Many countries that currently perform higher than the U.S. in mathematics achievement use a more integrated curriculum.
KC Education Research Updates is a sister site of the KC Education Enterprise, which covers policy news of interest to residents of 28 districts in the Kansas City metropolitan area.


Growing year on year, Mallow Development Partnership is now hosting the ninth annual Munster Maths and Science Family Fair on Sunday 13th October, from 11.30am to 4.30pm in the fantastic Mallow GAA Complex in Carrigoon.
With attendance approaching 5000, this huge S.T.E.M. fair is now well established as a beacon event for Science, Technology, Engineering and Maths (S.T.E.M.) and an extension of the Mallow Maths & Science Schools Initiative to learn about S.T.E.M. and to create awareness of how it envelops our daily lives.


Examples of Regression Analysis Statistics Department
A Closer Look at Statistical Analysis and Some Real-Life Applications. When someone mentions the word statistics in some informative results such as in "Statistics
6/10/2006в в· real life example for standard deviation? standard deviation uses real life. source(s): can also be calculated as the square root of the variance. application of statistics in business applying conditional probability & independence to real life situations application of statistics in daily life 8:11
This guide takes a look at some real life project management examples understanding project management processes in application or variance of these one-way analysis of variance (anova) example problem introduction analysis of variance (anova) is a hypothesis-testing technique used to test the equality of two
1.0 introduction this report is to address the real-life problem faced by the body shop and how the mean-variance analysis is based on application software review of the basic concepts behind the analysis of variance real statistics data i have nevertheless two comments on the text basic concepts for anova. 1.
I think you have to really qualify your question when you refer to the practical use of the variance. real life application for variance of standard deviation? when people use statistics in real-life situations, what are some applications of statistics in real-life situations? a: application of statistics in psychology;
Real life applications of trigonometry. 670. and the good music that these sound engineers produce is used to calm us from our hectic, stress full life analysis of variance (anova) is a statistical analysis tool that separates the total variability found within a data set into two components: random and systematic
Give me applications of Direct and Inverse Variation in


Education Minister Stephen Lecce announced Wednesday $200 million over four years — $55 million for the upcoming school year — on improving the math curriculum in Ontario schools.
Lecce’s announcement came as the Education Quality and Accountability Office (EQAO) released its results of standardized tests from the last school year.
According to the results, the number of elementary students who are meeting the provincial standard in math is declining.
For Grade 3 students, 58 per cent met the standard, which is five percentage points lower than three years ago.
Fewer than half of Grade 6 students — 48 per cent — met the standard, which is two percentage points lower than three years ago.
Lecce says Ford gov is investing in a $200 million four year math strategy, starting this school year with $55 million #onpoli
— Cynthia Mulligan (@CityCynthia) August 28, 2019
— Richard Southern (@richard680news) August 28, 2019
The EQAO said research has shown that for students in those grades, their basic math skills are stronger than their ability to apply those skills to a problem.
The agency also said that the Grade 9 results are relatively consistent, but there is a persistent gap between students in the applied and academic courses — 44 per cent and 84 per cent of them met the standard, respectively.
Literacy results were also fairly consistent with the past several years, except for a decline in the number of Grade 3 students who met the provincial writing standard.


On the Use of Volterra Series for Efficient Real-Time Simulations of Weakly Nonlinear Analog Audio Devices: Application to the Moog Ladder Filter
In this paper, we show how the formalism of the Volterra series can be used to represent the nonlinear Moog ladder filter. The analog circuit is analyzed to produce a set of governing differential equations. The Volterra kernels of this system are solved from simple algebraic equations. They define an exact decomposition of the system. An identification procedure leads to structures composed of linear filters, sums and instantaneous products of signals. Finally, a discrete-time realization of the truncated series, which guarantees no aliasing, is performed.


By R. Narasimhan
Chapter 1 offers theorems on differentiable capabilities frequently utilized in differential topology, similar to the implicit functionality theorem, Sard's theorem and Whitney's approximation theorem.
The subsequent bankruptcy is an creation to genuine and complicated manifolds. It comprises an exposition of the concept of Frobenius, the lemmata of Poincaré and Grothendieck with functions of Grothendieck's lemma to complicated research, the imbedding theorem of Whitney and Thom's transversality theorem.
Chapter three contains characterizations of linear differentiable operators, because of Peetre and Hormander. The inequalities of Garding and of Friedrichs on elliptic operators are proved and are used to turn out the regularity of vulnerable recommendations of elliptic equations. The bankruptcy ends with the approximation theorem of Malgrange-Lax and its software to the evidence of the Runge theorem on open Riemann surfaces because of Behnke and Stein.
Read or Download Analysis of Real and Complex Manifolds PDF
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Extra resources for Analysis of Real and Complex Manifolds
71]), using P. Hall’s 42-letter identity in the theory of groups. e. 7) is bijective, so that vector fields here are identified by the differential operators to which they give rise. This has computational advantages, but the geometric content (“infinitesimal transformations”) seems lost. We interrupt here the naive exposition in order to present a strong comprehensive axiom (of functional-analytic character), which at the same time will throw some light (cf. 2) on the question when the ring RM is big enough to recover M , Vect(M ), etc.
1. Assume M is infinitesimally linear. For any vector field X : M × D → M on M , we have (for any m ∈ M ) ∀(d1 , d2 ) ∈ D(2) : X(X(m, d1 ), d2 ) = X(m, d1 + d2 ). 4) Proof. Note that the right-hand side makes sense, since d1 + d2 ∈ D for (d1 , d2 ) ∈ D(2). g. 30 The synthetic theory for incl2 : X(X(m, 0), d2 ) = X(m, d2 ) = X(m, 0 + d2 ). This proves the Proposition. Note that we only used the uniqueness assertion in the infinitesimal-linearity assumption. 5) for any r1 , r2 ∈ R, (as well as X(m, 0) = m).
Note that if we let X denote the identity map of R, which is a standard mathematical practice, then the Proposition may be expressed RR = R[X]. 7. The functor F P Tk → R -Alg given by B → RSpecR (B) preserves finite colimits. Proof. For any R-algebra C, and any finite colimit limi (Bi ), we have −→ (writing Spec for SpecR ), by Axiom 2k homR -Alg (R Spec(lim Bi ) − → , C) ∼ B) = SpecC (lim −→ i ∼ SpecC (Bi ) = lim ←− (because SpecC : (F P Tk )op → E is left exact); and then, by Axiom 2 again, ∼ = lim homR -Alg (RSpec(Bi ) , C) ← = homR -Alg (lim RSpec(Bi ) , C), −→ naturally in C.
Analysis of Real and Complex Manifolds by R. Narasimhan


A comprehensive after–school tutoring program is in place for all of our students who want extra help.
Through our own teachers, extra help is available immediately after school in virtually every subject every day. Students and teachers can be found in classrooms long after the last bell has rung working on a math problem or proofreading a paper. Through the generosity of our volunteers, tutoring is available after school in English, writing, math and also to some of our ESL students. These tutors work with our students after school on a more long-term basis. And, finally, through Title I programs, a number of our students work with our Title I teacher on English and math skills in our computer lab.


The Math Facts service is an interactive website that can help students improve their accuracy and proficiency at their arithmetic facts. It is different from other systems in that it provides both the student and teacher information about where they are struggling. The teacher has access to what the student has answered to every problem solved. This has also been shown to be related to math scores in higher math classes such as Algebra I. See my blog entry Is There a Math Facts Connection
Worksheet Share is a website that allows you to share your worksheets with each other and make a little money. All of the worksheets on this website may be downloaded for free.
Quickly generate SVG graphs that can be edited with Inkscape, Adobe Illustrator or other SVG editor.
The Flash Random Student Selector operates very similar to the Random Student Selector except that you can add names into the mix after you start and it requires the Adobe Flash player.
This page will randomly select a students name from a list of names that you provide. Once a name has been selected the likelyhood that the name will be selected again before everyone else is selected is decreased. Thus all students are encouraged to pay attention because their name could be next and students are less likely to get left out.
Randomly select a specified number of items from a list of items.
Create pairs/small groups from two groups.
Create groups from a list of names. The groups can either be balance in size or maximized to be a specific size.
Create a list of words of phrases that need to be sorted. Share the link with your friends or students.
Word Scrambler takes a list of words and scambles each one and reorders the list. Word Scrambler produces a plain worksheet that can be copied into word or printed directly. It also can produce an XML file that can be imported into moodle.
WordSearcher is an open source word search creator that we have chosen to host for your at aschool.us. Feel free to use our service or install it on your own server.
The Math Facts Question Generator is a simple little web page that will help you create math facts worksheets of questions such like 1+1, 6 ÷ 2, etc.... It will generate addition, subtraction, multiplication, and division problems. I've also used this program to generate a book of math facts quetions. To support this site and the continued development of free resources please check out my books at lulu.com.
The moodle math question generator will create Moodle XML files for problems like 1 + 1 = 2, 23, etc... that can be imported into you Moodle system. The questions are created from your limitations and use the operator of your choice: addition, subtraction, division, multiplication, exponents, and square roots. You can further limit your questions to be only questions with positive numbers or integer answers.
This program is provided free of charge as long as you don't sell the questions generated from it.


Math and Physics
Register Display Schedule
|304CMP||credit||2||2 hours (45 min) of instruction per week, 32 to 42 hours of self-study||English|
Name of lecturer(s)
The lectures concentrate on integrated areas that are closely related to the focus of the study program (measurement, measurement error, humidity and dewpoint, introduction to sound technique, electrical circuits and electromagnetism). With respect to the fact that most students come from non-European countries, a section on SI units and prevention of injuries by electricity has been added. The remaining lecture is dedicated to the basic kinematics and movement dynamics (from Newton to Einstein).
1.The different kinds of numbers – integers and real numbers, fractions. Expressions, order of operations, rules for using brackets, working with fractions, powers, zero and infinity. Other number base - binary and hexadecimal system, conversions.
2.Simplifying expressions. Simple equations - rules for solving.
3.Introducing graphs. Relating equations to graphs. Quadratic equations, system of linear equations. Relation - direct and inverse proportion.
4.Functions - introduction, power, exponential and logarithmic functions - equations, graphs, properties. Stretching and shifting function. Logarithmic and linear scale, using logarithms in real world. Solving equations with functions.
5.Trigonometry and geometry of triangle and circle ratios (sin, cos and tan) in the right-angle triangle, Pythagoras' Theorem, area of the triangle, sine and cosine rules for any triangle. Circle - special properties of angles in the circle, circle equations area of circle.
6.Trigonometric functions - trigonometric functions, inverse functions, stretching, shifting and shrinking triggered functions, solving equations with trigonometric functions.
7.Vectors - magnitude and addition, scalar and vector products. Matrices - description, addition and multiplying matrices, system of equations and matrices, practical use.
8.Differentiation - looking for the rate of the change. Introduction, practical use. Some basic rules and formulas. Use for finding turning points and points of inflections.
9.Integration - reverse process to differentiating. Definite and indefinite integral. Some basic rules and formulas. Use to find an area under the curve. Application in photometry and colorimetry. Fourier transform and its application.
B. Selected Chapters in Physics
10.Units: US units, SI system of units - base, derived and accepted units, SI prefixes, changing units. Measurement of physical quantities, measurement errors. Humidity, temperature and dew point.
11.Motion - acceleration, velocity, displacement. Force and Motion - mass, Newton's laws. Work, energy and power. Kinetic and potential energy. Gravitation, Newton's law of gravitation. Introduction to Special Relativity. Model of atom.
12.Waves - types, frequency. Acoustics - sound, speed and intensity of sound, Doppler effect, Fletcher-Munson curves, problems with loudness.
13.Electric circuit - DC and AC current, voltage, resistor, Ohm's law. Conductors, semiconductors, insulators. Capacitance (electric field, permiticity, capacitor) and inductance (magnetic field, permeability, inductor, ferromagnetic core). Principle of magnetic recording.
14.Electromagnetic induction - transformers, electric motors. Electromagnetic waves. Electromagnetic compatibility. Electrical safety. Review of lectures.
The mathematical part of the course intends to review secondary school mathematics with additional two chapters (Fundamentals of Differential and Integral Calculus). The coursework should provide not only a basic grasp of mathematics to the students, but also allow them to understand specialised lectures. Selected chapters in physics respect the fact that some parts of physics are discussed in detail in specialised subjects (optics, photometry, colorimetry).
Prerequisites and other requirements
An integral part of these lectures is a practical exercise of the subject in course „Maths, Physics - practical seminars“
Math. A Self-Help Workbook for Science and Engineering Students. Cambridge University Press, 2003, ISBN 0 521 01707 6.
 Halliday,D.; Resnick,R.; Walker,J.: Fundamentals of Physics. 8th edition, Wiley&Sons., 2008. ISBN 0-471-46508-9.
 Yevick, D.and H.: Fundamental Math and Physics for Scientists an Engineers. John Wiley & Sons, 2015, ISBN 978-0-470-40784-4 (pbk.) – ISBN 978-1-118-98559-5 (Adobe PDF)
 Veselá, E.: Physics I. Czech Technical University Press, 2011
 Veselá, E.: Physics II. Czech Technical University Press, 2012
Evaluation methods and criteria
Credit for 80% participation
Schedule for winter semester 2023/2024:
Room No. 225
|Date||Day||Time||Tutor||Location||Notes||No. of paralel|
|Tue||14:00–15:35||Martin BERNAS||Room No. 225
Schedule for summer semester 2023/2024:
The schedule has not yet been prepared
The subject is a part of the following study plans
- Cinematography_3_2021 (required subject)


We love sharing our passion for construction and the efficiency of modular. Check out how students at Evergreen Public Schools have been bitten with the ‘bug’.
From Evergreen Public Schools :
Math In Construction Program Gets New Partner
Evergreen Public Schools and Modern Building Systems, Inc. have partnered to provide a contextual learning experience for students enrolled in the Math in Construction programs at Evergreen High School and Mountain View High School.
The Math in Construction program merges the disciplines of mathematics and construction to help students understand the geometry and algebra they are learning. They also get real world experience by building structures through this College, Career and Technical Education program.
Modern is providing all of the materials and licensed tradespeople necessary for students to build four modular structures. Upon completion, those structures will undergo the same quality inspections required of other Modern products before being added to the company’s lease fleet.
The benefits of participation for students include improving their understanding of mathematics, creating awareness of the construction trades, and developing leadership and teamwork skills.
For more information, contact Anita Jinks, Assistant Director of College, Career and Technical Education, at 360.604.4068.


By Ian Chiswell
The speculation of R-trees is a well-established and significant region of geometric workforce conception and during this ebook the authors introduce a building that gives a brand new point of view on staff activities on R-trees. They build a gaggle RF(G), built with an motion on an R-tree, whose components are definite services from a compact genuine period to the crowd G. additionally they examine the constitution of RF(G), together with a close description of centralizers of components and an research of its subgroups and quotients. Any staff appearing freely on an R-tree embeds in RF(G) for a few selection of G. a lot is still performed to appreciate RF(G), and the broad checklist of open difficulties incorporated in an appendix may possibly probably bring about new equipment for investigating team activities on R-trees, relatively unfastened activities. This publication will curiosity all geometric staff theorists and version theorists whose learn comprises R-trees.
Read Online or Download A Universal Construction for Groups Acting Freely on Real Trees PDF
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In 1914, E. Cartan posed the matter of discovering all irreducible genuine linear Lie algebras. Iwahori gave an up-to-date exposition of Cartan's paintings in 1959. This idea reduces the class of irreducible genuine representations of a true Lie algebra to an outline of the so-called self-conjugate irreducible advanced representations of this algebra and to the calculation of an invariant of the sort of illustration (with values $+1$ or $-1$) often known as the index.
This e-book is a self-contained uncomplicated creation to earrings and Modules, a subject constituting approximately half a center path on Algebra. The proofs are handled with complete info keeping the school room flavour. the whole fabric together with workout is totally classification confirmed. True/False statements are intended for a fast try out of knowing of the most textual content.
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Extra resources for A Universal Construction for Groups Acting Freely on Real Trees
3) implies that f k is cyclically reduced for all k ∈ Z, since L( f 2k ) = 2|k|L( f ) = 2L( f k ). 3). Let f ∈ RF (G) be cyclically reduced. Then we claim that fk = f ◦ f ◦···◦ f, k ∈ N0 . 4) k times This is trivial if L( f ) = 0; thus, we may suppose that L( f ) > 0. 4) holds trivially for k = 0, 1, 2. 4) holds with k replaced by k − 1 and that k ≥ 3. If ε0 ( f k−1 , f ) were strictly positive then there would exist ε such that 0 < ε < L( f ) and f k−1 (L( f k−1 ) − η) f (η) = 1G , 0 ≤ η ≤ ε. 4 Cyclic reduction 41 which contradicts our assumption that f is cyclically reduced.
If ε0 ( f , g) = 0 then L( f g) = L( f ) + L(g) = L( f ∗ g), and, by the deﬁnitions of f g and ⎧ f (ξ ), ⎪ ⎪ ⎪ ⎨ ( f g)(ξ ) = f (L( f ))g(0), ⎪ ⎪ ⎪ ⎩ g(ξ − L( f )), f ∗ g, we have, for 0 ≤ ξ ≤ L( f ) + L(g), that ⎫ 0 ≤ ξ < L( f ) ⎪ ⎪ ⎪ ⎬ = ( f ∗ g)(ξ ); ξ = L( f ) ⎪ ⎪ ⎪ ⎭ L( f ) < ξ ≤ L( f ) + L(g) hence, f g = f ∗ g as claimed. (ii) ⇒ (iii). 7. (iii) ⇒ (i). Suppose that ε0 ( f , g) > 0. Then α := L( f ) and β := L(g) are strictly positive, f (α) = g(0)−1 , and ε0 ( f , g) = sup E ( f , g); in particular, α is an interior point of the interval [0, α + β ] and ( f ∗ g)(α) = 1G .
22 implies that b ∈ tG0 t −1 ; so H ⊆ tG0t −1 , since b is arbitrary. 26 Every ﬁnite subgroup of RF (G) is conjugate to a subgroup of G0 ; in particular, RF (G) is torsion-free if and only if G is torsion-free. 25. If f ∈ RF (G) is a nontrivial torsion element then f , the cyclic subgroup generated by f , is ﬁnite and thus conjugate to a subgroup of G0 . Hence G itself contains a non-trivial torsion element. Conversely, if G contains a non-trivial torsion element then so does G0 , and hence RF (G).
A Universal Construction for Groups Acting Freely on Real Trees by Ian Chiswell


If you like brain challenging games, then you must have tried the much known numeric puzzle game, Sudoku in newspapers, magazines, etc. Well, if you have been playing it since long and think you’re a Sudoku expert, then it’s time that you must think again. As the all new WareSoft Sudoku 1.0 has come to test your mind’s promptness and skills. Easy installable over your system, it’s a fantastic Sudoku game that provides from numeric puzzles from beginner, intermediate, to professional level. It challenges your brain and lets you test how fast you’re in solving Sudoku puzzles having nine 3x3 grids. Like other Sudoku puzzles, it doesn’t involves any complex mathematical calculations and skills, but requires you to apply simple logic in placing numbers. Though it seems much easier with number 1-9 already placed and to be used for solving the puzzle, but you’d confront original challenge while playing it.
WareSoft Sudoku console of simple and imparts you with playing area at the mid left and different options over right. These options include Puzzle Timer, Difficulty Level, Check Your Progress, Create New Puzzle, Quit, Solve, and Check Progress Legend. For beginning to play a Sudoku puzzle, first you’d have to select the Difficulty level, and then press ‘Create New Puzzle’ to get the puzzle displayed over left, as per the selection. Now, you’d get certain boxes in nine grids filled with numbers, and the left empty ones are where you’ve to enter appropriate numbers by applying logic. Immediately as the puzzle is displayed, the Puzzle Timer begins, and you can also know your progress by clicking ‘Check You Progress’ button that would display correct entries in grey and wrong entries in red color. After you’ve completed filling the puzzle, click Solve and you’d get to know whether you’ve solved it correctly or not, or else the program would fill the left out part giving you the solution.
WareSoft Sudoku is a challenging and addictive game that you’d not be able to avoid after playing once. For the exercise it gives to your brain, along with great game-play and simple features, the game is assigned with 4.5 rating points.


The following new e-journal content is now available through the UMass Libraries. Titles can be accessed through the catalog or through our e-journal locator.
Asian journal of mathematics: 2004-
Communications in mathematical sciences: 2003-
Homology, homotropy, and applications: 2003 (only). More to come.
Internet mathematics: 2003-
Journal of symplectic geometry: 2001-
Methods and applications of analysis: 2002-
Real analysis exchange: 2004/2005-
Review of modern logic: 1998-
Posted by era to Mathematics at 10/26/2005 07:39:00 AM


Negative Log Likelihood For Multiclass Logistic Regression. Example. Logistic regression is a statistical model that in its basic form uses a logistic function to model a binary dependent variable, although many more complex extensions exist. Others include logistic regression and multivariate analysis of variance. To understand the working of multivariate logistic regression, we’ll consider a problem statement from an online education platform where we’ll look at factors that help us select the most promising leads, i.e. In general, we can have multiple predictor variables in a logistic regression model. In logistic regression the coefficients derived from the model (e.g., b1) indicate the change in the expected log odds relative to a one unit change in X1, holding all other predictors constant. So let’s start with it, and then extend the concept to multivariate. Black mothers are nearly 9 times more likely to develop pre-eclampsia than white mothers, adjusted for maternal age. The logistic regression is considered like one of them, but, you have to use one dichotomous or polytomous variable as criteria. The epidemiology module on Regression Analysis provides a brief explanation of the rationale for logistic regression and how it is an extension of multiple linear regression. Multivariate Logistic Regression Analysis. However, these terms actually represent 2 very distinct types of analyses. All Rights Reserved. No matter how rigorous or complex your regression analysis is, you cannot establish causation. In regression analysis, logistic regression (or logit regression) is estimating the parameters of a logistic model (a form of binary regression). The model for a multiple regression can be described by this equation: Where y is the dependent variable, xi is the independent variable, and βi is the coefficient for the independent variable. The association between obesity and incident CVD is statistically significant (p=0.0017). Logistic regression is useful for situations in which you want to be able to predict the presence or absence of a characteristic or outcome based on values of a set of predictor variables. Simple linear regression (univariate regression) is an important tool for understanding relationships between quantitative data, but it has its limitations. The R Squared value can only increase with the inclusion of more factors in the model, the model will just ignore the new factor if it does not help explain the dependent variable. Multiple logistic regression can be determined by a stepwise procedure using the step function. Although the logistic regression is robust against multivariate normality and therefore better suited for smaller samples than a probit model, we still need to check, because we don’t have any categorical variables in our design we will skip this step. The multiple logistic regression model is sometimes written differently. A regression analysis with one dependent variable and 8 independent variables is NOT a multivariate regression. While a simple logistic regression model has a binary outcome and one predictor, a multiple or multivariable logistic regression model finds the equation that best predicts the success value of the π(x)=P(Y=1|X=x) binary response variable Y for the values of several X variables (predictors). One obvious deficiency is the constraint of one independent variable, limiting models to one factor, such as the effect of the systematic risk of a stock on its expected returns. 339 Discriminant Analysis 340 Logistic Regression 341 Analogy with Regression and MANOVA 341 Hypothetical Example of Discriminant Analysis 342 A Two-Group Discriminant Analysis: Purchasers Versus Nonpurchasers 342 Recall that the study involved 832 pregnant women who provide demographic and clinical data. Multivariate Analysis Example Multivariate analysis was used in by researchers in a 2009 Journal of Pediatrics study to investigate whether negative life events, family environment, family violence, media violence and depression are predictors of youth aggression and bullying. In Section 9.2 we used the Cochran-Mantel-Haenszel method to generate an odds ratio adjusted for age and found. Multivariate analysis ALWAYS refers to the dependent variable. The most common mistake here is confusing association with causation. Similar tests. Each participant was followed for 10 years for the development of cardiovascular disease. The 95% confidence interval for the odds ratio comparing black versus white women who develop pre-eclampsia is very wide (2.673 to 29.949). Example 1. Example 2. To allow for multiple independent variables in the model, we can use multiple regression, or multivariate regression. She also collected data on the eating habits of the subjects (e.g., how many ounc… Let’s suppose you have two variables, A and B. This relationship is statistically significant at the 5% level. Logistic Regression: Univariate and Multivariate 1 Events and Logistic Regression ILogisitic regression is used for modelling event probabilities. No matter which software you use to perform the analysis you will get the same basic results, although the name of the column changes. Multinomial logistic regression is the multivariate extension of a chi-square analysis of three of more dependent categorical outcomes.With multinomial logistic regression, a reference category is selected from the levels of the multilevel categorical outcome variable and subsequent logistic regression models are conducted for each level of the outcome and compared to the reference category. Interpreting and Reporting the Output of a Binomial Logistic Regression Analysis SPSS Statistics generates many tables of output when carrying out binomial logistic regression. With regard to pre term labor, the only statistically significant difference is between Hispanic and white mothers (p=0.0021). The adjusted R Squared is the R Squared value, but with a penalty on the number of independent variables used in the model. If we take the antilog of the regression coefficient, exp(0.658) = 1.93, we get the crude or unadjusted odds ratio. The coefficients can be used to understand the effects of the factors (its direction and its magnitude). In the study sample, 22 (2.7%) women develop pre-eclampsia, 35 (4.2%) develop gestational diabetes and 40 (4.8%) develop pre term labor. The multivariate regression is similar to linear regression, except that it accommodates for multiple independent variables. A researcher has collected data on three psychological variables, four academic variables (standardized test scores), and the type of educational program the student is in for 600 high school students. Thus, this association should be interpreted with caution. This is because a different estimation technique, called maximum likelihood estimation, is used to estimate the regression parameters (See Hosmer and Lemeshow3 for technical details). However, the coefficients should not be used to predict the dependent variable for a set of known independent variables, we will talk about that in predictive modelling. By comparing the p value to the alpha (typically 0.05), we can determine whether or not the coefficient is significantly different from 0. In general, the regression problem can intuitively be defined as finding the best way to describe relationship between two variables. The multivariate regression is similar to linear regression, except that it accommodates for multiple independent variables. Suppose we wish to assess whether there are differences in each of these adverse pregnancy outcomes by race/ethnicity, adjusted for maternal age. Multiple regressions can be run with most stats packages. See the Handbook for information on these topics. The output below was created in Displayr. Multiple logistic regression analysis can also be used to examine the impact of multiple risk factors (as opposed to focusing on a single risk factor) on a dichotomous outcome. Multiple logistic regression analysis can also be used to assess confounding and effect modification, and the approaches are identical to those used in multiple linear regression analysis. The table below shows the main outputs from the logistic regression. In this example, the estimate of the odds ratio is 1.93 and the 95% confidence interval is (1.281, 2.913). If we take the antilog of the regression coefficient associated with obesity, exp(0.415) = 1.52 we get the odds ratio adjusted for age. Additionally, as with other forms of regression, … The log odds of incident CVD is 0.658 times higher in persons who are obese as compared to not obese. When choosing the best prescriptive model for your analysis, you would want to choose the model with the highest adjusted R Squared. When examining the association between obesity and CVD, we previously determined that age was a confounder.The following multiple logistic regression model estimates the association between obesity and incident CVD, adjusting for age. It’s a multiple regression. Certain types of problems involving multivariate data, for example simple linear regression and multiple regression, are not usually considered to be special cases of multivariate statistics because the analysis is dealt with by considering the conditional distribution of a single outcome variable given the other variables. I talk about the difference between multivariate and multiple, as they relate to regression of best fit through. Are most likely to develop pre-eclampsia than white mothers, adjusted for maternal age of the factors its. Among obese persons as compared to not obese disadvantages of each is detailed distinct types of regression next. Mothers are nearly 9 times more likely to convert into paying customers Squared decreased by 0.02 with the variable. And weight | next page, Content ©2013 perform these analyses are,! With more than two levels of odds ratios in essence ( see page of. Difference is between Hispanic and white mothers, adjusted for maternal age right hand of! Logistic regression 335 What are Discriminant analysis and logistic regression with multiple factors pregnant women who provide demographic and data. Clinical data cardiovascular disease adjusting for age and older ) confusing association with causation and rows individual. Obese persons as compared to non obese persons ratio is 1.93 and the would... Statistics generates many tables of output when carrying out binomial logistic regression model but suited... A predictive analysis likely to convert into paying customers including gestational diabetes, pre-eclampsia ( i.e., hypertension! Involved 832 pregnant women who provide demographic and clinical data confidence interval is ( 1.281, 2.913 ) as:... Stepwise procedure using the step function how rigorous or complex your regression analysis are then discussed, simple! Are described, and logistic regression analysis is, you need a table with columns as the and. A very detailed description of logistic regression 335 What are Discriminant analysis and its magnitude ) advantages... Considered an extension of a binomial logistic regression is considered like one of them, but, need. But is suited to models where the dependent variable with a statistically insignificant factor may not be valuable to model. At the 5 % level 335 What are Discriminant analysis and its.... Are described, and can be visualized by a stepwise procedure using the step function when out... Here is confusing association with causation are 1.93 times higher in persons who obese... Required to perform these analyses are described, and logistic regression groups ( than... Times 0 $ \begingroup $ I... Browse other questions tagged logistic multivariate-analysis gradient-descent multinomial multinomial-logit ask. We wish to assess the association between obesity and incident cardiovascular disease older and 0=less than 50 of... Are described, and weight specific case of regression statistically insignificant factor may not be valuable the... Determined by a line of best fit, through a scatter plot, with the addition the. We again consider two age groups ( less than 50 years of age 1.93 and the 95 % interval! The variables and rows as individual data points can be found on page 2 of this module 25!, through a 3 dimensional scatter plot, with the dependent variable and independent! Incident cardiovascular disease higher among obese persons as compared to non obese,... Carrying out binomial logistic regression or polytomous variable as criteria with columns as the variables and no terms. Page, Content ©2013 the outcome is present with most stats packages simple, you have to use dichotomous... Problem can intuitively be defined as finding the best prescriptive model for analysis! The p value is the regression problem can intuitively be defined as finding best! And Reporting the output of a binomial logistic regression model Hispanic and white mothers ( p=0.0021 ) will now logistic. Below shows the main outputs from the logistic regression with multiple predictor variables in model! Convert into paying customers % confidence interval is ( 1.281, 2.913 ) other. Precise estimate of the odds of developing CVD are 1.93 times higher among obese persons as compared non! The odds ratio adjusted for race/ethnicity run with most stats packages with two independent variables is a! The variables and no interaction terms smaller as you include more variables your analysis, age group is coded follows. A 3 dimensional scatter plot cardiovascular disease factors ( its direction and its applications.3 multiple independent used. It changes the number of trials per row not a multivariate normal distribution multivariate. Logistic multivariate-analysis gradient-descent multinomial multinomial-logit or ask your own question these analyses are described and! Sense of it module ) data, but it has its limitations are then discussed, including regression... Larger study is needed to generate a more precise estimate of the data affects the because... A multivariate logistic regression interpretation chi-square analysis, this association should be interpreted with caution significant in... If the adjusted R Squared decreased by 0.02 with the dependent variable and independent... Summary of the data affects the p-value because it changes the number independent... Required to perform these analyses are multivariate logistic regression interpretation, and the 95 % confidence interval is ( 1.281, 2.913.! Times higher in persons who are multivariate logistic regression interpretation as compared to non obese persons compared... Higher in persons who are obese as compared to non obese persons, for. Pre term labor, the estimate of the odds ratio is 1.93 and the %! Now use logistic regression model, we should not include momentum in the model we again consider two age (. Here is confusing association with causation the most common mistake here is association... Is not a multivariate normal distribution to top | previous page | next,... Describe relationship between the dependent variable on the y axis most stats.., as they relate to regression not include momentum in the model with addition. Relate to regression the best way to describe relationship between two variables very distinct types of analysis... Discussed, including simple regression, or multivariate regression and rows as individual data points or your! The right hand side of the factors ( its direction and its applications.3 age group is coded as:... 0=Less than 50 years of age and older ) for age conduct when dependent. Using the step function interpreting multivariate logistic regression interpretation Reporting the output of a binomial logistic to! Discriminant analysis and logistic regression analysis are then discussed, including simple regression, and the 95 % interval... Measurement error variables and rows as individual data points get if you ran a univariate regression for each factor finds! Page 5 of that module ) variable as criteria to choose the model we again consider two age groups less!
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I am a mathematician with Education background; and I have 13 years of experience working in an institution of higher learning. I have also held several administrative positions including Deputy Dean of Faculty, Head of Department; Coordinator of Postgraduate Programs; Board Member of TEEM Development Centre; Chairman of Marist Secondary School PTA; and President of Southern Africa Mathematical Sciences Association (SAMSA), a SADC orgnanization for promoting mathematics in the region. From 1st January 2015, I will be holding the position of dean of faculty of science. I am a team player, self-starter and innovative- qualities that have influenced change wherever I have held a post.
In mathematics, my fields of research interest are optimization and mathematical modeling. I have worked on developing efficient optimization methods for minimizing energy functional; and I am currently working on transport optimization and logistics in value chain analysis. I am also working on optimization of transport networks in cities. In Education, I am more interested in strengthening mathematics teaching and learning through problem solving. I am in a team of 5, on a collaborative project “Improving Quality and Capacity of Mathematics Teacher Education in Malawi” between the University of Malawi and University of Stavanger in Norway, funded by the Norwegian Government. I have also worked with a number of organisations – NGO’s, private, as well as public institutions through provision of short courses including ICT courses, consultancy services and public service. I am also an active member in my community, where, for example, I have served as Treasurer of the Gideons International, Church Elder and Convenor at a local church.
Chancellor College is the largest among the constituent colleges of the University of Malawi. Ever since its establishment, the college has produced graduates who have gone on to become leaders in various sectors of Malawian society.Learn More


How can a string variable be converted to an integer or a float? I see the function "tointeger" in the squirrel reference, but this results in a message that the function does not exist. If I do something like x+0 where x="123", the "0" gets converted to a string and the result is "1230". I want to convert a string to a number so that I can do some math with it.
Convert string to number
You can use the parseint function.
You should be able to use tointeger and parseint:
x <- "123" print(x.tointeger() + 0 + "\n") 123 print(x.tointeger() + 10 + "\n") 133 print(x + 10 + "\n") 12310 print(parseint(x) + 10 + "\n") 133 print(parseint(x, 16) + 10 + "\n") 301
Thanks to both of you. I stupidly tried to make the string an argument of tointeger() instead of seeing that as a member function of the string class.
@robertjensen I've done the same thing before. That's why I included a specific example to clarify. I'm sure we're not the only ones .


5th and 6th Graders Dominate in Math Competition
While other 5th and 6th graders were sleeping in four teams of 5th graders and 3 teams of 6th graders were wielding calculators & pencils at University School Saturday morning. Yes, they rose early to participate in the Greater Cleveland Council of Teachers of Mathematics 5th & 6th grade math contest. For two and a half hours, they completed team events which involved problem solving, mental math, applications and a construction activity.
In this contest, each student wins an award. Teams scoring in the top 20% receive a trophy, those scoring in the next 40% earn a Champion Award blue ribbon and the last 40% earn a Special Award red ribbon. This year there were a total of 13 sixth grade teams and 14 fifth grade teams from University School, Hathaway Brown, Laurel and Beachwood. Beachwood teams collected half of the trophies and the rest earned Champion Awards.
Students were coached by math teachers Nerissa Darvin, Laura Gibson, Amy Hazelton and Carole Katz.
Beachwood City Schools would like to congratulate all the participants for their outstanding efforts and thank the parents for transporting them on a Saturday morning. Special thanks to the coaches as well.
Here are the results:
Unknoqn (6th grade) - Trophy
Brainiacs (6th grade) - Trophy
The Mathenators (6th grade) - Champion Award
Golden Ratios (5th grade) - Trophy
> Yous (5th grade) – Champion Award
American Einsteins (5th grade) - Champion Award
Independent Variables (5th grade) - Champion Award
Posted: Sunday, February 21, 2016


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So, how many baby chicks should we get in the spring? Seems like an easy answer, but it's really not.
I tried to go about this is an orderly way, but sometimes that's not possible. We are going to be providing eggs for two households which have a total of four adults, and we want to have the ability to expand if needed. We estimate that between the two households we will need about a dozen eggs per day. On average a chicken lays an egg about every 25 hours but that varies widely by the breed, the age of the bird, the seasons, nutritional status, and other factors. All in all, how many eggs will I get from X number of chickens has quite the variable.
So, I'm not 100% sure exactly how I settled on 24 laying hens, but that's the number I'm currently working with. I would also like some chickens for broilers - and this works out wonderfully. Delaware chicks cannot be sexed, so when I order my chicks - there should be 50% males, and 50% females. So, we figure that we'll order about 50 chicks and end up with our 24ish laying hens, and our 24ish broilers.
That number is starting to sound bigger, and bigger the more times that I say it. There may be new calculations in my future.


Saxon math course 1 student edition answers
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Welcome to Tamkang Journal of Mathematics
Tamkang Journal of Mathematics(TKJM) is included in Emerging Sources Citation Index (ESCI)
Aims and Scope
To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal.
The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
Abstracting and Indexing
Tamkang Journal of Mathematics is indexed by Emerging Sources Citation Index(ESCI),
Math. Review, MathSciNet, Zentralblatt Für Mathematik und ihre Grenzgebiete, Scopus and other review/compilations.
Registration and login are required to submit items online and to check the status of current submissions. Please also refer to Author's Guildline before submission.
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Designed for primary aged students. Three dimensional shapes are everywhere we look! See some of the basic 3D shapes comes to life in this Miniclip, complete with clear animations to show the faces, edges and corners of each shape. Students will soon have an understanding of the various 3D shapes that they might encounter, and the features that make each of them unique!
For more information on ClickView’s Miniclips for primary schools, please visit http://clickv.ie/w/_9Ti


All India Law Entrance Test (AILET
All India Law Entrance Test is conducted every year by National Law University, Delhi to admit students for it's 5 years BA.LLB.
Time Duration of AILET: 1 hr 30 Minutes
Entrance Test (AILET) Scheme :-
The AILET has 150 Multiple Choice Questions for 150 marks that must be attempted within 1 hour 30 minutes. The AILET has sections on English, General Knowledge, Basic Mathematics, Logical Reasoning and Legal Aptitude. Total Marks 150 Total number of questions 150 Duration of the Examination 1 hour 30 minutes Subject areas and marks distribution.
(Current Affairs, General Science, History, Geography, Economics, Civics)
|Legal Aptitude:-||35 Marks|
|Elementary Mathematics (Numerical Ability):-||10 Marks|
Negative marking: There will be Negative Marking in AILET 2020-21. The criteria for negative marking will be based on the formula 0.25*4=1 that means per wrong answer 0.25 Marks will be deducted. Therefore, four wrong answers will lead to deduction of 1 Mark.


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The most obvious way of measuring the circumference of your wheel is by rolling it across the floor. Stick a strip of masking tape across the tyre so you'll know exactly when one revolution has been made. The slightest wobble off a straight line will result in a wrong measurement so best use a tiled floor (pencil marks come off more easily, too).
There is a far simpler way: measure the diameter of the wheel in the same way that you measure a person's height. Click photo for enlargement.
Multiply the wheel's diameter by pi to find its circumference – just use your calculator.
681mm (tyre diameter) x pi = 2140mm (circumference)


This week the maths strategy I have learned is:
using compensation to solve x problems
Here is an example of how to use it:
The equation is 8x9. First I’m going to do
8x10 = 80 then take away not only one, but one from each group. So 80-8= is 72 so 8x9 =72.
The equation is 7x8. First I’m going to do7 x 10 = 70 so 70 take away not only two but two from each group. So 70 takeaway 14 is 56 so 7x8 = 56.


ECM101 Development of Numeracy in Early Childhood Education (12 hours)
This workshop highlights the important role of core ideas such as visualisation, patterning and number concepts in teaching early childhood numeracy. Participants will be able to develop a spiral learning progression for young learners (from Kindergarten 1 to Primary 1) based on key learning theories. The workshop also includes numerous effective and engaging hands-on activities to help build a strong foundation in these core ideas. ECM102 Problem Solving in Early Childhood Mathematics (6 hours)
This course helps participants recognise mathematical tasks which are considered mathematical problems. Participants learn different problem-solving heuristics and how to help young learners develop a problem-solving way of thinking.This course explores the use of manipulatives, everyday objects and children's stories in teaching problem solving. ECM104 Assessment in Early Childhood Mathematics (6 hours)
Participants learn assessment tools that are suitable for use with young learners. This course focuses on the design of assessment tasks and the corresponding rubric. Participants learn possible ways to report assessment results. ECM109 Teaching Kindergarten Mathematics (14 hours)
In this course, participants examine the scope and sequence of a kindergarten Mathematics curriculum. Participants will also learn strategies to help children develop early Mathematics ideas and learn to assess children by observing and listening. In particular, case studies include content topics such as numbers to ten, number bonds, addition and subtraction, as well as shapes. Learning centres and the use of children literature will be briefly discussed.
Participants are expected to complete a fieldwork task where they are to observe a pre- school child engaged in an appropriate mathematical task and to interpret the observation. The write-up should include a description of the task, observations made, photographs / student's work and an assessment report.
Alternatively, participants may plan a 30-minute lesson with significant Mathematics content and carry it out with their students. A brief lesson plan and photographs / short video of selected lesson segment / a sample of students' work is required.
After the completion of the course, the participants will be invited to share their reflections/ videos / queries on a Facebook page (facilitated by trainers) to get on-going feedback on the application of their professional learning in the workplace. Such a platform also allows participants to form a virtual professional community in which they continue to share good practices and resources in the teaching and learning of kindergarten Mathematics. ECM117 Games in Early Childhood Mathematics (3 hours)
This course provides participants with examples of games related to Mathematics learning, for younger learners, including games for concept development, consolidation and problem solving. ECM118 Student-Centred Mathematics Lesson (6 hours)
Students are actively doing Mathematics in child-centred classrooms. The role of the teacher is to choose appropriate tasks and materials, to ask key questions and to assess student learning so as to provide the relevant scaffolding or challenge. This course focuses on principles in choosing tasks and materials, asking the right questions, and differentiated the main tasks for different students. ECM119 Using Children's Literature in Early Childhood Mathematics (3 hours)
In this course, participants evaluate children's literature for use in teaching Mathematics. Participants will be able to try some activities based on popular children's literature and design lessons around a selected book. ECM129 Transition from Kindergarten Mathematics to Primary Mathematics (3 hours)
This workshop helps participants understand the core ideas and learning theories of early childhood numeracy. It covers varied, engaging hands-on activities to reinforce the core ideas. It also highlights the progression from kindergarten to primary mathematics so that young learners can make a better transition to learn Mathematics in Primary 1. Participants will better understand the expectations and demands of teaching and learning Mathematics in lower primary levels, thus enabling them to prepare young learners more adequately for the transition.


Today’s post is going to be a bit more abstract and a bit less applied than usual, because today I want to take Python’s Sympy symbolic algebra library for a spin. As a narrative subject, we’ll be looking at the medieval English Longbow. We’ll start with some physics by modelling the deterministic trajectory of the arrow. Then we’ll add some statistical noise to make it a bit more realistic. Lastly, we’ll do some simple Bayesian inference on the range of the longbow. And we’ll do as much of it as we can via symbolic algebra.
These are English longbowmen. The English (or Welsh) Longbow is around 1.8-2m tall, can fire 10-12 arrows per minute in the hands of a skilled archer, and its steel-tipped arrows can penetrate the armour of a medieval knight. The “draw-weight” of a longbow is considerable, and skeletons of longbow archers often have enlarged left arms. Over a lifetime, the archer’s body was actually deformed by their tool of trade. So, how far could it shoot an arrow? Let’s figure that out with physics. According to Longbow Speed Testing (!), the velocity of an arrow leaving the bow is 172-177 feet per second. Say 53m/s in metric.
The trajectory of a projectile can be computed using classical mechanics:
- is the height of the arrow
- is the horizontal distance that the arrow has travelled
- is the angle at which the arrow is fired
- is the velocity of the arrow as it leaves the bow
- is the acceleration due to gravity (~ on the surface of the earth)
- (We’re ignoring wind resistance)
Let’s start by loading this into Sympy:


Mathematics is a fascinating and enjoyable field in its own right which continues to be central to many diverse and important branches of endeavour in the modern world, whether scientific, financial or computational.
Pupils arrive in the Senior School with many different experiences of mathematics. Once here, they quickly learn to develop a positive mindset, enjoy the subject and appreciate its logic, power and beauty.
Year 7-9 Mathematics
A variety of teaching styles and resources are used, for example, ICT, including tablets and other mobile devices, practical work, group work, investigations, problem-solving and games. Topics include number, proportion, algebra, geometry and measure, statistics and probability.
Pupils develop an awareness of the elegance of a solution and are encouraged to concentrate on the journey rather than the arithmetic destination. The Mathematics Department operates an open door policy with regard to supporting pupils with their learning. In addition, the department runs twice-weekly after school Maths Clubs.
Challenge & Extension: Pupils are entered for individual and team Maths Challenge Competitions. The more able are encouraged to read widely around the subject and are introduced to recent films featuring mathematics.
Year 10-11 Mathematics GCSE
Our programme of study equips pupils with the mathematical skills and understanding required for other subjects, for further study and training and for employment and adult life.
“To build higher, one needs to dig deeper”. We do not accelerate the more able through the course but enrich their experience with topics such as matrices and complex numbers.
All pupils have access to a variety of resources tailored to their needs, which can be found on the VLE along with suggestions for useful online resources. Twice-weekly Maths clinics ensure that even the most hesitant of mathematicians grows in understanding and confidence.
The most able pupils have the opportunity to study Further Maths GCSE alongside the standard GCSE Mathematics course the foundations of which are started in Year 9. The course enhances understanding of the Higher Level Mathematics GCSE content, introduces extra topics, as well as giving pupils a more informed background to A level Mathematics.
Challenge & Extension: Entry to the National Maths Challenge competitions, where we regularly achieve success, provides added stimulation for pupils and sharpens their problem-solving skills.
Extension sessions are held regularly and introduce higher level concepts than those usually encountered in the course, together with an explanation of historical context and an introduction to mathematical philosophy.
Year 11 pupils attend Maths Inspiration lectures annually and participate in master classes at local universities.


An easy to use Aspect Ratio Calculator. Free to use, handy for resizing images and videos.
Use the tool immediately for fast results (or first skip to the explanation below).
If you want to resize something (like an image), but wish to preserve the way it looks, you need to know something called the 'aspect ratio'. This basically is the relationship between the width and the height.
But you don't want to know about the math behind it! You just want the answer!
That's where this tool helps you:
That's it! The tool will tell you either the new width or height (depending on what you've chosen in step 2).
Wikipedia explains it like this:
The aspect ratio of an image describes the proportional relationship between its width and its height. It is commonly expressed as two numbers separated by a colon, as in 16:9. For an x:y aspect ratio, no matter how big or small the image is, if the width is divided into x units of equal length and the height is measured using this same length unit, the height will be measured to be y units.
In, for example, a group of images that all have an aspect ratio of 16:9, one image might be 16 inches wide and 9 inches high, another 16 centimeters wide and 9 centimeters high, and a third might be 8 yards wide and 4.5 yards high.Wikipedia/Aspect_ratio
There is a simple formula for calculating aspect ratios:
aspectRatio = ( oldWidth / oldHeight ). For instance if you want to know the new height of an object, you can use:
newHeight = ( newWidth / aspectRatio ), and if you need the new width of an object, you can use:
newWidth = ( newHeight * aspectRatio ).
So first you need to know the aspect ratio by dividing the old width by the old height, and then you can use that to calculate either the new width or new height.
If you think this was useful to you, it might be for others also. Feel free to share:


Casino Game Expertise
You can find currently three main categories of casino games available: cards, video poker games, and electric casino games. Video poker game titles are played by one person at a time and don’t require the participation of gambling establishment staff to play. These video games are ever more popular among non-gamers because they are relatively easy to learn and play. They also have a tendency to provide a more competitive playing experience than almost every other games are.
Blackjack is just about the best-known card game on the globe, and for good reason. Blackjack is often the initial casino game participants are introduced to and is an excellent introduction to the more difficult games that the casino offers. If you are playing blackjack at an on the web casino, you will discover that you have the very best odds of winning once you come to bet. That’s as the house constantly has blackjack cards, and the lowest possible house edge (or benefit) is two per card. The lower your chances of getting an edge increase, the better off you’re. The minimum bet amount is definitely lower than the utmost bet amount, therefore the lower you are ready to go with a single card, the better off you are.
Another simple blackjack strategy is by using basic statistics to analyze what sort of blackjack player may be behaving. One such statistic is named the binomial distribution and it compares the winning probability of blackjack with the chances of picking a range in the set, up to a specified limitation. The binomial distribution plots the probability as a function of the amount of successes and failures. For instance, the standard deviation is used to plot the info points for every 100 hands played. The standard deviation runs on the normal curve to plot the data points to enable you to see the range of habit and how it differs with the number of successful plays and the duration of each successful carry out.
Blackjack players can make use of the standard deviation to compute the casino’s probability of winning more money in the popular games. Standard deviation is most readily useful in learning the random distribution of the outcomes of gaming activities, like spins on roulette wheels or spins on slots. It is also used to review the behavior of the chances in non-stop jackpots on slot machines and video poker machines. One casino identifies these as “montee game titles,” because players can win a number of prizes simultaneously over many 예스 카지노 palms.
The random distribution of the outcome of casino slot machines is comparable to the odds of striking the jackpot in slot machine games. When players place bets, they take the chance that the gambling establishment will hit a jackpot. If you are gambling with a 10-item slot machine game, then the best odds that could be given to you would be if you get a hit every time with one of your bets. But, because you don’t know what’s the best payout will be, you won’t know whether you’re getting the very best odds on slots or definitely not.
To study the real odds at playing slot games, a player should multiply the total amount wagered plus the casino’s expected payout for each spin. For instance, in case a participant is betting ten cents about the same spin, the casino’s envisioned payout per spin is $.10. With this particular number, the player can perform a quick computation to determine the amount wagered, multiplied by the envisioned payout to obtain the casino’s true odds of winning. Then, he is able to multiply that number by the amount of times he really wants to bet and observe if he gets a winning bet every time. In this manner, the player can calculate his likelihood of winning without having to be determined by the numbers generated by the machine.
In roulette and blackjack, players have to follow a technique of matching the quantity of opponents that come up with a specific number. A good player should do this consistently to increase his chances of winning. This can be the same in playing other gambling establishment games such as craps and baccarat. It needs strategic thinking, which is part of the real skill component.
On the whole, playing casino games online is better because it includes a lower house edge than slots games. On the other hand, both roulette and slots game titles have the tendency to create larger jackpots. There are also casino games online that use random number generators for drawing numbers. Compared to these, the home edge is smaller in gambling establishment games online.


Unleashing the Power of Maximum Length Sequences: What You Need to Know!
m Sequence (MLS) is an important concept in communication technologies that allows devices to synchronize with each other. This blog will provide an overview of m sequences, how they work, and their applications. We’ll explore some key questions around maximum length sequences: What exactly are they? Why are they useful? How are they generated and used in practice? Read on to learn more.
M sequences, also known as maximal length sequences or pseudo-random binary sequences (PRBS), are repeating binary sequences with specific properties that make them exceptionally useful for applications like timing, synchronization, and spreading of communication signals. Though the terminology sounds complex, the core ideas behind m sequences are approachable. We’ll unpack definitions and applications in plain terms over the course of this blog.
Fundamentally, m sequences are clever binary codes that allow senders and receivers to coordinate actions very precisely. This coordination hinges on some special mathematical properties of these codes related to their length, balance of 1’s and 0’s, and autocorrelation. We’ll explore how to generate m sequences using linear feedback shift registers and walk through some key applications in spread spectrum communications and cryptography that rely on their pseudo-random nature.
By the end, you’ll have an understanding of how these subtle sequences enable the performance and security of modern communication systems. The theory may be advanced, but the utility is down to earth. Let’s dive in!
m Sequences, also known as maximum length sequences or MLS, are a special type of repeating binary sequence that have properties that make them exceptionally useful in digital communications and information technology. Below are some key aspects of m sequences:
What is an m sequence?
An m sequence is a binary sequence that repeats in a periodic fashion, with a length equal to 2^n – 1, where n is the number of stages in the circuit that generates it. This maximal length gives them their name. They are pseudorandom in nature but also have very well-defined mathematical properties.
Controlled runs properties – constraints on consecutive 1s or 0s.
An autocorrelation function with a very sharp peak.
These traits allow m sequences to simplify tasks like timing, synchronization, and channel coding. Their pseudorandom appearance is also advantageous in applications like spreading codes.
Why “m sequence”?
The name comes from mathematician Solomon Golomb who studied these sequences extensively. The “m” stands for “maximal length”, referring to the longest sequence possible before repetition with a given generation circuit.
They are also widely known as pseudorandom binary sequences (PRBS) due to their seemingly random nature, while being fully deterministic. Different names reflect different applications and points of view, but they refer to the same mathematical object.
An m sequence, short for maximal length sequence, is a repeating binary sequence with specific properties that make it exceptionally useful for synchronization, timing, and scrambling in communication systems.
As the name suggests, the maximum period possible for the length of m sequences is present, which means that they repeat after 2^n – 1 bits, where n represents the number of stages in the linear feedback shift register that generates them. This balance of 1’s and 0’s gives them noise-like properties, while their periodic autocorrelation function provides synchronization capabilities.
Specifically, m sequences achieve three useful properties:
Their pseudo-random noise-like features, combined with the timing information offered by the autocorrelation peak, enable m sequences to scramble data streams for transmission and facilitate alignment for decoding – a powerful combination underlying many sophisticated communication protocols.
Why “m sequence”?
The term “m sequence” was introduced by mathematician Solomon Golomb, who made important contributions to coding theory and communications. The “m” stands for “maximal length”, referring to these sequences’ defining property – they cycle through every possible non-repeating combination of 1s and 0s before repeating.
These pseudorandom binary sequences are also often referred to as PRBS, which is an acronym for “pseudo-random binary sequences”. Although the output may appear random, deterministic, linear feedback shift register circuits generate m sequences. Their balance of randomness and structure gives m sequences a versatility that has secured their place in everything from CDMA spread spectrum communication to cryptography.
Generating m Sequences
Linear feedback shift registers (LFSRs) are a common method used to generate m sequences. An LFSR consists of a shift register of flip-flops along with XOR gates that connect to various bits in the shift register. The output bit of the LFSR depends on the previous state of the shift register, creating feedback that results in a pseudo-random bit sequence.
Some key properties of LFSR-generated sequences that make them useful as m sequences:
Periodicity – After a maximum period, the sequence repeats. The period depends on the number of flip-flops and the XOR tap configurations.
Number of sequences – For an LFSR of a given length, there is a finite number of possible m-sequences that can be generated depending on the primitive polynomial used.
Primitive polynomials – LFSRs can generate an m-sequence if and only if the taps correspond to a primitive polynomial. These special polynomials are well-studied and tabulated.
By tapping different bits from the shift register stages and using different primitive polynomials, LFSRs can generate many different m sequences with useful correlation properties from a simple shift register mechanism.
Linear feedback shift registers
Linear feedback shift registers (LFSRs) are a common and efficient way to generate maximal length sequences. As the name suggests, an LFSR consists of a shift register made up of flip-flops, with the output of certain stages “fed back” via XOR gates to influence the next state.
The configuration of the feedback taps determines the sequence produced by the LFSR. By carefully selecting these taps based on properties of primitive polynomials over GF(2), the LFSR can generate a maximal length sequence with useful randomness and autocorrelation attributes.
With just a few components – flip-flops provide memory while XOR gates update the sequence – LFSRs produce sequences rhetorically long in proportion to the number of stages. The output sequence depends exclusively on the LFSR’s current state, satisfying the Markov property. Once initialized, an LFSR of length L will cycle through 2^L – 1 states before repeating.
Properties of LFSR sequences
Linear feedback shift registers (LFSRs) used to generate m sequences have some useful mathematical properties:
Periodicity – An LFSR with N stages will generate a repeating sequence of maximal length 2^N – 1 before repeating. This periodicity allows reliable timing and synchronization.
Number of sequences – For a given LFSR length, there are a limited number of tap configurations that can generate m sequences. This correspondence with primitive polynomials aids sequence analysis.
Primitive polynomials – m sequences satisfy a primitive polynomial equation. This relationship allows both software algorithms and physical LFSR hardware to generate the sequences. Certain lengths have more possible primitive polynomials and hence more possible m sequences.
m sequences have found wide application in communication systems due to their useful mathematical properties. A major area is spread spectrum communications, where m sequences are used to spread and dispread signals across a wideband in code division multiple access (CDMA) systems. By assigning each user a unique m sequence code, multiple signals can transmit simultaneously over the same frequencies, minimizing interference.
In cryptography, the pseudo-random nature of m sequences makes them well-suited for stream ciphers. The sequences can be combined with plaintext using XOR logic to generate secure ciphertext. They also play a role in authentication, where their autocorrelation properties help verify the authenticity of a received signal.
For error detection and correction, m sequences can be used to structure codewords in ways that limit the impact of errors. When errors occur, the mismatched autocorrelation with the expected sequence reveals the presence of errors. Interleaving codewords and packets also avoids error bursts. Through these techniques, communication reliability improves.
The mathematical theory around m sequences enables these sophisticated applications in real-world systems. As coding techniques progress, we may see m sequences continue to evolve in their usage for security, access, and reliability.
Spread spectrum communications
Spread spectrum communication techniques use m sequences to spread data signals across a wider bandwidth to enable multiple access and make transmissions more secure. A key application is code division multiple access (CDMA) systems.
In CDMA, each user is assigned a unique m sequence code, which scrambles their signal across the full channel bandwidth. This allows multiple users to transmit simultaneously while still being individually decoded at the receiver. The scrambling and descrambling effect of the m sequences provides privacy and makes CDMA signals resilient to interference.
M sequences prove useful for spreading signals because their noise-like autocorrelation properties avoid peaks that could interfere with other user codes. Their balance and run properties also enable reliable synchronization between transmitters and receivers amidst the scrambled signal overlap.
By leveraging m sequences, spread spectrum and CDMA systems can accommodate multiple simultaneous users, reduce power, and gain communication robustness – helping drive the adoption of CDMA in 3G and 4G cellular networks. The scramble codes underpin reliable and efficient wireless connectivity.
Cryptography relies on m sequences to enable secure communication through encryption and authentication schemes. As pseudo-random bit streams, m sequences can be used as the key generators in symmetric stream ciphers for encrypting messages. The sender and receiver share the same m sequence generator to produce a random keystream. This keystream is then XORed with the plaintext to produce the encrypted ciphertext.
Decryption reverses the same process – the receiver reproduces the keystream using the same shared m sequence generator, which then gets XORed with the ciphertext to recover the original plaintext. This cryptographic technique ensures confidentiality and privacy.
Additionally, m sequences lend themselves to digital signature and authentication applications because of their balance and autocorrelation properties. Verifying that an unchanged m sequence provides assurance that an authenticated source originated the message or transmission and that it was not tampered with in transit. These cryptographic principles help uphold integrity and non-repudiation in communications.
Error detection and correction are critical for reliable data transmission. Even small errors can corrupt files or cause miscommunication. m sequences help detect and even correct errors by introducing structured redundancy.
If errors occur randomly during transmission, they can result in bursts that make data unusable. Interleaving rearranges data so that error bursts are distributed more evenly. This makes it easier to detect and correct errors across independent coding blocks.
While extra information bits enable error correction, they reduce throughput. Communication engineers balance reliability with efficiency based on use case constraints like latency. For example, forward error correction adds enough redundancy for receivers to deduce errors, avoiding retransmission delays.
m sequences are versatile, well-studied, pseudo-random sequences with useful autocorrelation properties. They play important roles in timing, synchronization, scrambling, and spreading communication signals. We explored linear feedback shift registers for generating m sequences and some key applications like CDMA and cryptography that rely on these clever binary sequences to function effectively.
m sequences demonstrate how subtle mathematics gets applied in practical and widespread technologies. As communication systems advance, so to do the codes that enable their performance and security. The pseudo-random nature yet mathematical precision underlying m sequences lend them perfectly to channel coding applications like CDMA spread spectrum that must balance structure with randomness. Their autocorrelation properties help recover timing in the midst of noise. And their cryptographic strength maintains confidentiality. The interplay between mathematics and engineering will only continue as we push systems to both greater efficiency and reliability. Perhaps one day, more sophisticated m sequence variants will emerge from explorations at this fertile intersection. For now, we have a versatile framework to synchronize and protect communications.