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MATH OF MACHINE LEARNING 2020
FEBRUARY 19-22, 2020
Sirius University of Science and Technology and HDI Lab of HSE University invite you to join Winter School aimed at undergraduate/graduate students and young postdoctoral fellows from pure and applied mathematics. Participants will learn about modern trends in machine learning with a strong emphasis on the mathematics behind them. This intense four-day workshop will consist of 3 interdisciplinary mini-courses by world-class scientists, poster session by participants and master classes by industrial partners. Key topics of the Winter School:
- Reinforcement learning
- Deep learning
- Computation optimal transport
- Statistical inference
Computational Optimal Transport
Optimal transport (OT) is a fundamental mathematical theory at the interface between optimization, partial differential equations and probability. It has recently emerged as an important tool to tackle a surprisingly large range of problems in data sciences, such as shape registration in medical imaging, structured prediction problems in supervised learning and training deep generative networks. This course will interleave the description of the mathematical theory with the recent developments of scalable numerical solvers. This will highlight the importance of recent advances in regularized approaches for OT which allow one to tackle high dimensional learning problems. Material for the course (including a small book, slides and computational resources) can be found online at https://optimaltransport.github.io/.
Mean-Filed Langevin Dynamics and Deep Neural Network
In reinforcement learning, we are learning how to act. This course will be an introduction to the models and mathematical tools used in formalizing the problem of learning and decision-making under uncertainty. In particular, we cover the mathematics of policy evaluation, planning, and learning
The winter school will be held at the Sirius University (Sochi, Olympiyskyi prospekt, 1, room: TBA)
Registration of any person willing to participate is mandatory. We provide accomodation for invited speakers and junior researchers (BS, MS, PhD and young postdocs) selected by the organisation committee. Since the number of places we provide is limited, participants have to submit a short CV (Eng. or Rus.). We also provide travel grants for young people from Russia. The organisation committee will carefully review all the applications and will proceed with the strongest candidates based on their skills and motivation.
Registration is closed.


Keywords: Calculus of Constructions, Higher Order Logic, Typed Lambda Calculus, Equational Logic, Rewriting Logic
Rewriting logic together with it's membership equational sublogic favors the use of abstract specifications. It has a flexible computation system based on conditional rewriting modulo equations, and via its initial semsntics it supports a very liberal notion of inductive definitions. Pure type systems, on the other hand, in particular the calculus of constructions, provide higher-order (dependent) types, but they are based on a fixed notion of computation, namely beta-reduction. This unsatisfying situation has been addressed by addition of inductive definitions (Ch. Pauline-Mohring 1993, Z. Luo 1994) and algebraic extensions in the style of abstract data type systems (Blanqui, Jouannaud, Okada 1999). Also, the idea of overcoming these limitations using some combination of membership equational logic with the calculus of constructions has been suggested as a long-term goal by Jouannaud 1998.
To close the gap between these two different paradigms of equational logic and higher-order type theory we are currently investigating the open calculus of constructions (OCC) an equational variant of the calculus of constructions with an open computational system and a flexible universe hierarchy. Using Maude and the ideas on the Calculus of Indexed Names and Named Indices (CINNI) and Uniform Pure Type Systems (UPTS), we have developed an experimental proof assistant for OCC that has additional features such as definitions and meta-variables. Maude has been extremely useful to explore the potential of OCC from the very early stage of its design. In addition, the formal executable specification of OCC exploits the reflective capabilities of Maude, yielding an computational efficiency that brings us closer the the goal of a unified tool for programming, specification and verification integrating equational logic, higher-order logic and dependent types.


As I was preparing to drop off my son to the final math exam for his current semester in Grade 10, I told him that if he got 100% on the exam I would pay for internet hook-up to Xbox 360 Live, something he has been pestering me about for weeks. I'm pretty sure he could get 100% on the exam if he exerted himself a bit. He already has a 90% average in math, and I think if he paid a bit more attention and wasn't careless in his calculations he could get 100% or very close to it.
His position is: what's wrong with 90%? Nothing is wrong with 90%, of course. But if he is already so close to the ultimate, wouldn't it make sense to push a bit harder?
I don't know. I don't want to make his life miserable. I can't say I was all that good at math myself (that means I was the worst math student, ever) so I can't hold myself up as a great example. My interest in math really started when I was in my thirties and started reading some of Isaac Asimov's books on math and sciences. The books were fascinating, and I then saw the error of my ways in not being more attentive in school and improving my performance in mathematics, physics and chemistry.
When I was in high school in the 1960's, math and science nerds were subject to considerable derision. Students who were heading for liberal arts degrees at university thought themselves superior and called the math and science students 'plumbers.' Of course, in the end, I'm sure that many of the fine arts students ended up working for those same 'plumbers,' who might have become engineers, inventors, or internet millionaires. I wonder who got the last laugh?
My son just got home from his exam and chatted with me via IM. Here's the conversation:
He: It went well.
Me: Just well, or realllllllllllllly well?
He: Really well.
I don't know what that means. Will it be another 90% or should I expect something a bit north of that?
I guess I'll just have to wait to find out.


AP Calculus ABThere is no summer assignment for AP Calculus ABSupplies:
Text: The book we use is: Calculus, Eighth Edition, Early Transcendentals, Single Variable. The authors are Anton, Bivens, and Davis. The ISBN is 0-471-48238-2 and it was published in 2005.References:Policies, Principles, and Practices
- A graphing calculator is required for this course. If you do not have one of your own, one will be provided. We will use the TI-84+CE for class demonstrations. All of the TI-84 calculators use the same operating system, so a TI-84+ Silver Edition, or an older TI-84, will work fine. Some other calculators may be used, but the student will be responsible for learning the operating system. Check the College Board website for a list of "AP" approved calculators.
- Binder with binder paper
- Graphing paper
- Ruler (with centimeters and inches)
- Colored Pencils (these are not required, but it is useful to have a few for graphing.)


Math and Science Night will be held at Hillcrest next week, on Wednesday, April 20th from 6:30 p.m. – 8:30 p.m. Your children won’t want to miss seeing the Starlab (indoor planetarium). There will be many other fun-filled room activities that bring math and science to life at our school. Join us for all of the MSN excitement this year!
Volunteers (adults and kids) are still needed to make this night a success. Please email co-chairs Neeta Shah, email@example.com or Georgia de Nolfo, firstname.lastname@example.org if you are able to help.


Photo taken: Sanssouci Palace, Potsdam, Berlin, 2017.
Department of Statistics, Texas A&M University
College Station, TX 77843-3143
Street Address: 155 Ireland Street
Office: 437 Blocker
Voice: (979) 845-3141
Fax: (979) 845-3144
Since January 2019, I have been working as an Instructional Assistant Professor in the Department of Statistics at Texas A&M University. Previously, I was as a Postdoctoral Fellow with Valen E. Johnson in the Department of Statistics at Texas A&M University. Before this, I worked as a Postdoc Research Assistant (2015 - 2016) under Martin Schumacher in the Institute of Medical Biometry at the University of Freiburg, Germany. I received my Ph.D. in statistics from Texas A&M University in 2015 under Raymond J. Carroll and Yanyuan Ma.
I wrote my PhD Thesis on "Nonparametric and Semiparametric Regression Modeling in Case-Control Retrospective Study Design".
My research interest is in unsupervised machine learning algorithms like clustering for various high dimensional data, where number of features is much larger than the number of samples (e.g, n << p). I am also interested in scalable algorithms which can be conveniently used for large n as well.
Awards and Honor
Refereed for Journals
1. Statistics and Probability Letters.
2. BMC Bioinformatics.
3. Statistics in Bioscience.
1. !st place in Distinguished Flash Talk, Annual Postdoc Symposium, Texas A&M University, 2018.
2. 3rd place in Poster Presentation, South Eastern Texas Chapter of American Statistical Association, 2018.
3. Boyd Harshbarger Travel Award for Southern Regional Council of Statistics, North Carolina, 2015.


At Isha Vidhya schools, teachers use interactive and engaging activities to teach students new lessons. These activities keep students attentive and eager to learn and promote comprehension. Read about some of these creative teaching techniques in our “Actively Learning” blog.
Boredom is alien to our students as our teachers ensure that new lessons are taught via an activity or interactively. Invariably, as part of teaching a new lesson, teachers also describe the accompanying activity that is specifically devised to cement comprehension.
Read about class activities that keep our students on their toes and help them learn with eagerness and ease.
UKG students of Isha Vidhya, Coimbatore participated in activities such as Light the Lamp, Hear and Find, Smell and Find, Touch and Feel, and Tasting Food to learn about the five senses in the ‘My Body & My Health’ class. Their curiosity kept them engaged and attentive because they sometimes had to guess the items with their eyes closed.
Class 2 students of Isha Vidhya, Erode arranged colorful flashcards to learn basic math like single and two-digit numbers, lower and higher numbers, and math symbols (< > =). Rather than learning from a book or copying what the teacher would have written on the blackboard, this was a welcome alternative as they learned at their own pace and as a group.
The class 4 science teacher of Isha Vidhya, Salem taught her students to make an elementary stethoscope using a rubber tube, funnel, tape, and balloon. Subsequently, they used it to hear and count each other’s heartbeats per minute. They learned about stethoscopes during this exciting activity that was actually a lesson.
The class 4 Power English teacher of Isha Vidhya, Dharmapuri read the lesson with actions and expressions and then made groups of students mime while she reread it. Students participated animatedly in this activity, which aimed to help them develop their skills in expressive body language.
Playing with Numbers
An Isha Vidhya, Erode teacher played a ball game with her students in classes 3–5 to improve their math and concentration. She first chose a constant number for adding, subtracting, or multiplying and then when she threw the ball to a student, she called out a random number. That student had to then mentally calculate the sum and call out the answer while returning the ball to her. This activity kept them mentally and physically agile.
A Market in the Class
The class turned into a marketplace when class 6 students of Isha Vidhya, Cuddalore participated in an activity to better understand the various vendors in the market and how buying and selling transactions happen. They nimbly sailed through the activity, er, lesson.
Proving the Value of pi
In a group activity, class 7 students of Isha Vidhya, Dharmapuri drew circles of different radii. Following their teacher’s instructions, they first measured the circumference and diameter of the circles with thread and then with a scale. They then divided the circumference by its diameter and were thrilled when everyone had the same answer and learned the formula in a breeze.


Chapter 0: What Is Algebra About?
Before algebra, we learn how to combine numbers by adding, subtracting, multiplying, and dividing according to the rules of arithmetic. To go in this book, you must know arithmetic.
Cartoon: Piece of Cake
If algebra is about combining numbers, then what is algebra about? To answer this question, begin with some ordinary arithmetic problems.......(cartoon) and rewrite those problems horizontally, along a line.To me, this book is ideal for adults wanting to teach their youngsters or for adults like myself needing to learn or freshen up algebra skills. Children who don't already know some algebra might need a bit of help through the cartoons, but it will certainly keep their interest.
What do you think? Would you keep going to tease your memory?
Thanks to the publisher for a review/feature copy of this book.


Congratulations to Ivoh, who has been chosen as Star Learner, for writing a superb letter which recounted his experiences during Entrepreneur Week. His smoothie making business was a roaring success and helped to raise nearly £120 for his group's chosen charity - www.bathcatsanddogshome.org.uk. Well done super star.
A good website to use to watch video clips of children’s authors’ suggestions for how to improve your writing.
Create your own comic strip! You can print or email your finished cartoon strip!
A website full of interactive games to support your language skills
Lots of maths puzzles and problems linked to the popular series of Murderous Maths books.
A fun interactive problem solving story for all the family. Can your maths skills thwart Dr Wick’s Evil Plan?
Activities to show your skills in all areas of maths
Mind-boggling games to challenge the best mathematicians at Paulton Junior School!
http://www.naturegrid.org.uk/pondexplorer/pondexplorer.html If you have no pond nearby, this site allows you to try pond-dipping online!
A variety of interactive games for you to play related to KS2 science.
Want to do some experiments at home? This site has hundreds of ideas for you to try!
A great website for you if you love space and the planets!


Our class has been doing algebra
If you know what alga bra patterns look like this is what it is.
So that's what it looks like.
If you have done an algebra pattern you will be an expert!
I'm going tell you how we made it.
First you get a hexagon shape that's plastic has a outline to keep the shape in.
Now get two colours that looks like this
and now you make a pattern like red' blue 'red' blue and just keep repeating it over and over again till you want to have another colour. then you just keep going on till the whole thing is done then you have finished algebra patterns.


Summer Mathematics Workbooks
Clifton Elementary Schools
The following problems and websites are designed to allow elementary students to practice math skills throughout the summer in a fun way!
Clifton Middle Schools
Students who are attending Christopher Columbus Middle School and Woodrow Wilson Middle School in September will participate in Summer Math Day, shortly after the re-opening of school. In preparation for this, they are expected to complete the Summer Math Activities for their appropriate grade level.
Students attending Clifton High School this September are required to complete their Summer Math Workbooks by school opening.


We have had a busy two weeks in Class 5!
Our class trip last week was great- the children thoroughly enjoyed themselves and participated so well in the workshop. The adults at the studios commented on their great ideas and behaviour. It was a fun and educational day out for all!
We have continued our new topic in English and all the children are hooked with our new book ‘Boy in the Tower’ – they have completed some amazing pieces of writing and have really thought about up levelling their work.
In maths this week we have moved onto Fractions – a favourite topic of mine! Some of the children who thought fractions were really tricky have started to really understand what to do with them! Times table Rock stars has also started this week and I am glad to say that Class 5 had the most amount of logins on the first day! Well done! This is a great app to help children with their times tables and division facts – One child has already played 77 games!!!
Just a quick remainder that ALL children need their swimming kits on Monday’s!!
Have a great weekend


520.624.7552 [email protected]
Carman Ryken is the Co-Principal of Paulo Freire Freedom School – University. Carman earned a degree in French and Math from Mills College. Carman began teaching math at PFFS-U in 2012 and has been a leader in project-based learning and competency-based learning during her tenure. Carman is a skilled facilitator who has served as a Critical Friends Group coach and leader of the math department. Carman has presented on social justice in math and project-based learning in math at academic conferences. She is passionate about math and is committed to the success of all learners.


19th-Century Drafting Compass
This 19th-century English drafting compass is made of iron. A drafting compass is a drawing tool that can be used to draw circles or arcs, and is typically made of metal. It can also be used for navigation, mathematics, drafting, and for measuring distance, or plotting a course on a map. This compass has two legs that are connected by a hinge, so they can be moved toward or away from each other to change the size of the circle. One of the legs has a spike with a sharp point at the end. The other would likely be dipped in ink and used to draw the circle. During the Renaissance, many attempts were made to build a universal tool for performing a variety of mathematical calculations. This need was especially important for the military, because new battle technology called for more precise mathematical knowledge. In 1597, Galileo (1564–1642), an Italian astronomer, achieved this goal by inventing the geometric and military compass. Over time, the model became more refined, and is now known as the drafting compass.


Numerical Linear Algebra, August-December 2016
When Tuesday and Thursdays morning from 8:30 AM to 10:00 AM
Where Department of Computational & Data Sciences, SERC building, Room 102, Seminar Hall
Office: Department of Computational & Data Sciences, SERC building, Room 205.
Office hours: Tuesday 3:00 PM-5:00 PM or by appointment.
Office: Department of Computational & Data Sciences, SERC building, Room 208.
Office hours: Tuesday 2:00 PM-3:00 PM.
Matrix and vector norms, floating points arithmetic, forward and backward stability of algorithms, conditioning of a problem, perturbation analysis, algorithmic efficiency, Structured matrices, Solving linear systems, Gaussian elimination, LU factorization, Pivoting, Cholesky decomposition, Iterative refinement, QR factorization, Gram-Schmidt orthogonalization, Projections, Householder reflectors, Givens rotation, Singular Value Decomposition, Rank and matrix approximations, image compression using SVD, Least squares and least norm solution of linear systems, pseudoinverse, normal equations, Eigenvalue problems, Gershgorin theorem, Similarity transform, Eigenvalue & eigenvector computations and sensitivity, Power method, Schur decomposition, Jordan canonical form, QR iteration with & without shifts, Hessenberg transformation, Rayleigh quotient, Symmetric eigenvalue problem, Jacobi method, Divide and Conquer, Computing the Singular Value Decomposition, Golub-Kahan-Reinsch algorithm, Chan SVD algorithm, Generalized SVD, Generalized and Quadratic eigenvalue problems, generalized Schur decomposition (QZ decomposition), Iterative methods for large linear systems: Jacobi, Gauss-Seidel and SOR, convergence of iterative algorithms, Krylov subspace methods: Lanczos, Arnoldi, MINRES, GMRES, Conjugate Gradient and QMR, Pre-conditioners, Approximating eigenvalues and eigenvectors.
We will attempt to cover the book by Biswa Nath Datta. Some material (especially the later part of the course) will be drawn from Trefethen & Bau as well. Notes will be posted as and when required.
- Numerical Linear Algebra and Applications, 2nd Edition, by Biswa Nath Datta
- Numerical Linear Algebra, by Lloyd N. Trefethen & David Bau III
Other useful texts to possess:
- Applied Numerical Linear Algebra, by James W. Demmel
- Matrix Computation, by Gene H. Golub & Charles F. Van Loan
- Functions of Matrices: Theory and Computation, by Nicholas Higham
- Accuracy and Stability of Numerical Algorithms, by Nicholas Higham
There will be a total of 15 homework due roughly weekly. Homework will be posted on this website and will be due on Wednesday before 5 PM. Late homework will not be accepted. The homework will consist of 3-4 written questions and couple of MATLAB/C++ exercises. Students are strongly encouraged to typeset their solutions using LaTeX/TeX (10% bonus points for submitting in LaTeX/TeX). To save trees, the students need to send their homework through email to with the subject reading NLA_2016_HW_#_firstname, where # needs to be replaced with the homework number (between 1 and 15) and firstname is to be replaced with your first name in lower case. Details on how to submit the computing part of the homework will be elaborated in the homework itself.
No collaboration is allowed for homework.
The grader will expect you to express your ideas clearly, legibly, and completely, often requiring complete English sentences rather than merely just a long string of equations or unconnected mathematical expressions. This means you could lose points for poorly written proofs or answers. Clear exposition is a crucial ingredient of mathematical communication. Clarity of thought and presentation is more important in mathematics & sciences than any other field. The only way to master exposition is by repeated practicing.
To use \(\LaTeX\), try any of the following online LaTeX compilers.
Each homework will have couple of computational exercises. Students must be comfortable with programming and are expected to have working knowledge in C++ & MATLAB. If not, they should be able to learn and immediately pick it up. Depending on the comfort level of students with coding, I may reduce/remove the coding part from the subsequent assignments or might have them as extra credit/bonus.
For C++ compilers, try any of the following (there any many other options if you google for "online compiler"). Pick your favorite one.
There will be roughly a dozen short (3-5 minutes) surprise quiz in class, which will used for marking attendance.
Midterm : October 4th, Tuesday in class.
Final exam : December 5th, Monday, from 3:00 PM to 5:00 PM.
There will be no make up exams. All exams will be closed book, closed notes. No internet/calculator allowed.
Below is a tentative calendar, which will be updated as we make progress in the course. The chapters mentioned below are from the book by Biswa Nath Datta (unless and otherwise stated explicitly).


The Kohia Centre is now selling practice assessment tasks for all externally assessed mathematics achievement standards, together with their associated assessment schedules.
- Level One Mathematics and Statistics (including MCAT)
- Level Two Mathematics and Statistics
- Level Three Statistics
- Level Three Calculus
The cost is $70 per level or $195.00 for a set of four. The school will be invoiced payable by the 20th of the following month.
Although every effort has been made to ensure the relevance of the content you may need to tailor this resource to your school’s needs.
There are 9 questions in this survey.


Bring your 4th-12th grade students to learn more about pursuing a career in Science, Technology, Engineering, and Math (STEM). The Summit includes continental breakfast and a full day of workshops on technology and career topics. Parents can also attend workshops on tuition for college and resources for paying for college through federal agencies that provide internships.
$10 - Patriot Members
$20 - Non- Patriot Members
For more information, call Patriots Technology Training Center at 301-925-9350 .


This week NYU hosted a Software Carpentry Bootcamp along with Berkeley and U. Washington (the other institutes in the Moore-Sloan data science environment). I sat in on the python classes (there were also classes in R). However, on Monday, there was a huge announcement from the BICEP2 collaboration about the observation of B-mode polarization in the CMB, which is considered a smoking gun for primordial gravitational waves predicte by inflation. That made it hard to concentrate on python, but I tried to merge the two. I noticed that BICEP2 made their likelihood curve public. I also noticed that they got a bit mixed up with their Bayesian and Frequentist statistics (at least the terminology), so that gave me an idea.
Here's a link to my iPython notebook on alternate BICEP2 error analysis
For convenience, embedded below (using the pelican liquid notebook plugin)
The BICEP2 error quoted on r is 0.2+0.07-0.05 (green below lines), and it looks like it's really a Bayesian shortest interval using a uniform prior on r. Let's see what the error bar looks like by using -2lnL < 1 (intersection of blue and red lines). The likelihood curve is shown here and they made the data public -- thanks BICEP2!
Populating the interactive namespace from numpy and matplotlib
import numpy as np from matplotlib import pyplot as plt
header = r.text.split('\n')[:12]
Convert the text into an array of floats.
rawLikelihoodData = r.text.split('\n')[13:]
likelihoodScan =  temp = [i.split('\t') for i in rawLikelihoodData] temp for x,y in temp[:-1]: likelihoodScan.append([float(x), float(y)]) likelihoodScan = np.array(likelihoodScan)
And the integral is ~1 (so it's like a normalized posterior including the bin width ie. prob/0.001)
Get shortest interval, it will be from [0.145,0.262] to get the 68% for 1$\sigma$
lmax = likelihoodScan[:,1].max() rpeak = np.where(likelihoodScan[:,1]==lmax)
rminBicep, rmaxBicep = rpeak,rpeak integral,cutoff=0.,lmax-lmax/1000 while integral<0.68: rRange = np.where(likelihoodScan[:,1]>cutoff) rminBicep=np.min(rRange) rmaxBicep=np.max(rRange) integral = np.sum(likelihoodScan[rminBicep:rmaxBicep,1]) cutoff-=lmax/1000 print '[%f, %f]'%( rminBicep, rmaxBicep)
plt.plot(likelihoodScan[:,0],likelihoodScan[:,1]) plt.plot(likelihoodScan[rminBicep:rmaxBicep,0],likelihoodScan[rminBicep:rmaxBicep,1],'g') plt.plot([rminBicep/1000.,rminBicep/1000.],[0.,likelihoodScan[rminBicep,1]],'g') plt.plot([rmaxBicep/1000.,rmaxBicep/1000.],[0.,likelihoodScan[rmaxBicep,1]],'g') plt.xlabel('r') plt.ylabel('Likelihood')
Fortunately, a constant factor on the likelihood cancels out in likelihood ratio (or difference of log likelihoods). So let's see what the typical $\Delta \log L$ or $\Delta \chi^2$ interval would look like.
minLogL = -2 * np.log(np.max(likelihoodScan[:,1])) rmin, rmax = 0,0 for r, l in likelihoodScan: if -2*np.log(l)-minLogL < 1: rmin= r break for r, l in likelihoodScan[200:]: if -2*np.log(l)-minLogL > 1: rmax=r break print '[%f, %f]'%( rmin, rmax)
plt.plot(likelihoodScan[:,0],-2* np.log(likelihoodScan[:,1])-minLogL) plt.plot([0,0.8],[1.,1.],'r') plt.plot([rmaxBicep/1000.,rmaxBicep/1000.],[0.,1.],'g') plt.plot([rminBicep/1000.,rminBicep/1000.],[0.,1.],'g') plt.plot([rmax,rmax],[0.,1.],'r') plt.plot([rmin,rmin],[0.,1.],'r') plt.xlabel('r') plt.ylabel('-2 ln Likleihood') plt.ylim([0,2]) plt.xlim([0.1,0.3])
So that's slightly different from the BICEP2 result. In terms of the Bayesian credibility, that interval corresponds to
Slightly different numbers and a different probabilistic interpretation, but luckily it doesn't change the profound result.
Assuming that the BICEP2 data are in the asymptotic regieme, then we can quickly estimate the statistical significance of the observation (testing the r=0 hypothesis).
significance = np.sqrt(-2*np.log(likelihoodScan[0,1]))
This was done during a Software Carpentry bootcamp at NYU, it's more of a fun python project than a critique of the BICEP2 result. Congratulations to BICEP2!


Fontana W, Stadler PF, Bornberg-Bauer E, Griesmacher T, Hofacker IL, Tacker M, Tarazona P, Weinberger ED and Schuster P
RNA folding and combinatorial landscapes
Phys. Rev. E 47:2083-2099, 1993
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In this paper we view the folding of polynucleotide (RNA) sequences as a map that assigns to each sequence a minimum-free-energy pattern of base pairings, known as secondary structure. Considering only the free energy leads to an energy landscape over the sequence space. Taking into account structure generates a less visualizable nonscalar ‘‘landscape,’’ where a sequence space is mapped into a space of discrete ‘‘shapes.’’ We investigate the statistical features of both types of landscapes by computing autocorrelation functions, as well as distributions of energy and structure distances, as a function of distance in sequence space. RNA folding is characterized by very short structure correlation lengths compared to the diameter of the sequence space. The correlation lengths depend strongly on the size and the pairing rules of the underlying nucleotide alphabet. Our data suggest that almost every minimum-free-energy structure is found within a small neighborhood of any random sequence. The interest in such landscapes results from the fact that they govern natural and artificial processes of optimization by mutation and selection. Simple statistical model landscapes, like Kauffman and Levin’s n-k model [J. Theor. Biol. 128, 11 (1987)], are often used as a proxy for understanding realistic landscapes, like those induced by RNA folding. We make a detailed comparison between the energy landscapes derived from RNA folding and those obtained from the n-k model. We derive autocorrelation functions for several variants of the n-k model, and briefly summarize work on its fine structure. The comparison leads to an estimate for k=7–8, independent of n, where n is the chain length. While the scaling behaviors agree, the fine structure is considerably different in the two cases. The reason is seen to be the extremely high frequency of neutral neighbors, that is, neighbors with identical energy (or structure), in the RNA case.


Points must be within the polygon, not on the boundary. Gromov-Witten theory of a locally conformally symplectic manifold and existence of Reeb orbits in a homotopy class. Vertices and endpoints falling within the cluster tolerance are snapped during the validate topology process. Second, I take the number of all the bridges, add one to it, and place this number at the head of the succeeding calculation.
Third, after the letters A, B, C, etc. See below for an explaination of the table and the insertion point. The Topology Sections Table holds an ordered list of boundary features. Upon each reconstruction, it is these features, and their relationships, that will be processed into the resultant polygon geometry for the topology The Wings Of The Dove V2 download for free. Section 1. Most chapters end with problems that further explore and refine the concepts presented , cited: A book of curves download pdf.
First, the manifold calculus of Goodwillie-Weiss has prompted recent, productive activity by connecting the study of long knots, configuration spaces, and operad theory notably, the little n-disks operad.
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There is an obvious yet undeveloped relationship between factorization homology and this embedding calculus Complex Topological K-Theory Cambridge Studies in Advanced Mathematics read for free. If the dangling tubes are connected together, you end up with a triple torus or genus 3 pacifier Figure This pacifier can be unglued to make two spheres connected by four wormholes in the sense of Figure 1.
The "hollow Earth" has a nice symmetry in terms of the octagon contracting to a quadrangle, and as well makes a more intuitive picture of the Moon inside of the Earth, or vice versa, but what it really shows is the many ways to look at things download. This means that when doing the remesh operation, the inserted items will be merged as one element with the original DynaMesh.
When holding the Alt key while inserting a mesh, ZBrush will consider it to be a Subtractive negative mesh. Related item. Print version: : ; ISBN: Summary A First Course in Computational Algebraic Geometry is designed for young students with some background in algebra who wish to perform their first experiments in computational geometry. Originating from a course taught at the African Institute for Mathematical Sciences, the book gives a compact presentation of the basic theory, with particular emphasis on explicit computational examples using the freely available computer algebra system, Singular.
Readers will quickly gain the confidence to begin performing their own experiments. Holdings information at the University of Warwick Library Requesting live circulation data Live circulation data is not available. Displaying live circulation data. Location of copy Shelfmark Availability Internet. Back to results Back to item. Aberystwyth University Library. University of Birmingham Libraries. In addition to student organizations, undergraduate and graduate students have access to prizes and awards through the department.
International Congress of Mathematicians: Geometry by Cambridge University Press - Issuu
As the third-oldest university in the United States and a private Ivy League institution, Yale University has had the time and financial means to greatly expand its academic influence. For a BA in mathematics, students are required to complete 10 term courses numbered or higher. The BS in mathematics has the same requirements; however, students must complete an additional two courses in the physical sciences. Core areas of algebra, real analysis, and complex analysis are covered in each program. At the Yale Graduate School of Arts and Sciences, some of the best mathematics programs at the graduate level are offered.
When the University of Michigan was founded at the flagship Ann Arbor campus in , one of the first four subjects taught was mathematics. After establishing a strong foundation in these areas, students then begin developing their own contributions to the field as they pursue more specialized work and dissertation writing.
Students benefit from 15 areas of research, as well as a long-term grant program for elite students interested in pursuing groundbreaking topics. The University of Toronto opened its first mathematics program in , and the school soon established itself as one of the leading math research institutes in Canada.
George UTSG. The Scarborough campus offers program streams for its students, including a comprehensive stream, a statistics stream, and a teaching stream. Graduate students can choose from an MS or Ph. Carnegie Mellon University was founded as a technical school in under the patronage of entrepreneur and industrialist Andrew Carnegie. Graduate students studying mathematics at Carnegie Mellon can earn a doctor of arts or a doctor of science in the subject.
Learners can also specialize in pure and applied logic or algorithms, combinatorics, and optimization — both interdisciplinary degrees offered in conjunction with the departments of computer science and philosophy and the Tepper School of Business. Undergraduate studies at the University of Tokyo are organized into 10 faculties, including the Faculty of Science. Knowledge of the Japanese language is not required for admission, but a lack thereof limits student participation throughout the program. Learners also gain the skills to teach math or continue onto graduate coursework in the field.
With little more than 50 years of academic history, the University of Warwick finds innovative ways to expand its services and leave a mark on the world of higher education. Contrary to other schools and research departments, Warwick combines pure and applied mathematical research to create a unique academic atmosphere and increased productivity in offering some of the best mathematics programs available. Without compromising quality, the department features one of the largest undergraduate student acceptance rates in the UK. The resume of Cornell University is impressive: a private endowment, a federal land-grant, membership in the Ivy League, and a partnership with the State University of New York system.
The undergraduate track offers a wide selection of courses through several mathematics majors and minor programs considered among the best mathematics programs in the world. Introductory courses are taught with the understanding that not all students are mathematically inclined. At the graduate level, students take an average of years to complete their studies. All 43 tenured and tenure-track faculty members are experienced and hold unique interests in research areas.
Through years of history, the department has several achievements worth celebrating. These include its support of women in mathematics since and prominent role at the quadrennial International Congress of Mathematicians since The current 55 full-time faculty members include two members of the National Academy of Science, two MacArthur fellows, and five Guggenheim fellows. The math department at UT Austin offers degree tracks in the form of bachelor of arts, bachelor of science, master of arts, and doctor of philosophy programs.
In addition to providing these many opportunities to connect mathematics to cutting-edge technology, UCSD places an uncommon emphasis on the social aspects of this objective field. The mathematics department utilizes over 60 faculty to teach roughly Ph. Consisting of 30 colleges and 12 departments, Peking offers a full range of courses at all academic levels.
International students are welcomed at the Department of Mathematics. Undergraduate math students at NUS can major in pure mathematics, applied mathematics, data science and analytics, or quantitative finance. Learners can also enroll in the special program in mathematics , which includes an advanced curriculum for passionate math scholars.
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The research track best serves undergraduate math majors who want to continue to doctoral study. A leading institution of higher education in Germany, the University of Bonn has dedicated itself to cutting-edge research and global outreach. Each of these institutes provides unique networking and study opportunities.
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Other national relationships include partnerships with the Max Planck Institute for Mathematics and the Hausdorff Center for Mathematics. The University of British Columbia houses 16 faculties, 18 schools, and two colleges. Undergraduate learners can major or minor in mathematics at UBC. Mathematics majors complete either a bachelor of arts or a bachelor of science; the latter offers learners the opportunity to double-major in education. The bachelor of arts degree includes a cooperative education option and a computing coursework requirement.
Doctorate students may complete their degrees in three to four years.
Learners can pursue a master of science or doctor of philosophy in mathematics at ANU. The master of philosophy in mathematical sciences curriculum emphasizes theoretical mathematics, while the master of science in mathematics focuses on building quantitative and computational skills. Of the higher education institutions in Japan, Kyoto University is the second-oldest and one of the most recognized in the nation. The department is responsible for the general mathematics education for all undergraduate students. Basic education in calculus, algebra, geometry, and analysis is emphasized.
At the graduate level, 24 Ph. Yoshida-jyuku and Yoshida-jyuku Senior are mathematics camps managed by the department where students can learn about advanced mathematics through lectures and seminars. UW-Madison also offers an interdisciplinary applied mathematics, engineering, and physics undergraduate program. Female graduate students can also join the Women in Mathematics at Wisconsin group.
Each school year, the department also conducts a talent search , posing five math questions to high school and middle school students from around the world to scout talented mathematicians and foster their skills. Brown University in Providence, Rhode Island offers mathematics courses and programs for students who are interested in math and want to dedicate themselves to the field. Students can join several mathematics clubs.


In the event that meteorology wouldn't work out for me, I'd be working as a technician at either ThyssenKrupp Elevator or Simplex Grinnell fire alarms.You would still likely need college schooling for those.. but in the engineering field in lieu of the meteorology field
If you do that, Trevor, you might as well just stick with Meteorology. I am taking the same pre-requisite math and physics classes as engineering majors
I have officially completed the Physics and Calculus sequence for my MET degree. Thank the good lord. Now, I just have to get through Differential Equations this summer and I'll complete all the difficult math (minus my actual meteorology classes) for my degree. Congrats! All that math will begin to make more sense when you start applying it to your Meteorology courses.
Most definitely. I'm looking forward to it, surprisingly. I learn things better when they are relevant (as I am sure most people do).
I've also axed my broadcast journalism minor. I absolutely hated it after one class! So, I've decided to minor in geography, which half of the classes are electives, which I am making weather-related.


Monthly Archives: February 2015
Different perspectives on building architecture for the global tech folks.
A “God’s algorithm” is an algorithm that produces a solution to a puzzle with the fewest possible moves. Researchers have determined that this number (known as “God’s number”) for the Rubik’s Cube is twenty moves. In other words, ANY Cube can be solved in twenty moves or less (which is notable, considering that there are approximately forty-three quintillion configurations).
Previous resident Nathan Phinney whilst at Floda made this wonderful info graphic, yes a real rubiks cube was involved and the full explanation of the info graphic can be found here.


Attendees of an NACM audio teleconference, April 25, 2007 got an opportunity to learn about key statistical concepts and tools that can provide a way to analyze and manage the financial accounts of companies. The teleconference, “Statistical Tools for Managing Accounts,” was presented by Jack Williams, a professor at Georgia State University College of Law, a director in the Financial Recovery Services Group at BDO Seidman, LLP and the Scholar in Residence at the Association of Insolvency and Restructuring Advisors.
“All data tells a story,” Williams said. He pointed out that statistical analysis is a way to determine trends and glean other information from a set of financial data. “Statistical techniques can help get a better prospective of customers,” he said. With statistics, he noted, customers could be evaluated with other like customers or with the industry as a whole. Williams pointed out that conducting statistical analyses does not necessarily require having a statistical background, just an understanding of the mathematical concepts they present. Statistics can measure central tendencies and the variability of different financial values. “Statistical tools are the steady hand maidens to the credit profession,” Williams said. “They are efficient and they are reliable.” However, he pointed out, “They won’t displace your discretion or your gut feeling.” “All professions use statistics to manage uncertainty,” he added.
Financial statement analysis can present the true picture of a company’s liquidity, it’s debt and it’s financial performance. Statistical ratios are a set of tools designed to help present this picture. For liquidity there are the current ratio, quick ratio, payables deferral period, working capital and short pays. For debt ratios there are debt to equity and times interest earned. The performance ratios include DSO period, inventory carry period, profit margin, ROA and ROE. Williams explained each of these ratios. “My research shows that short pays are a good indicator of liquidity problems,” he said. “All of those ratios are designed to show us if we’re going to get paid.”
Williams explained various statistical measures of averages that are used to summarize data—the mean, median and mode. “When we summarize data we lose some specificity, but it becomes more manageable.” The data and what one wants to get from their analysis determine what kind of average to use. The mean can be presented on an arithmetic, trimmed or weighted basis. He noted that a trimmed mean is one that discards outlying values in a data set. A weighted average is one that assigns a higher value to certain data elements. A median is the value where an equal number of data points are of higher and lower value. “Generally you should be going to the mean unless you have good evidence to use something else.” Williams also explained measures of variability in data such as range, quartile and percentile and standard deviation. He defined standard deviation as the dispersion of values around the mean. He then used some data sets to present and explain various types of statistical calculations and how they may be analyzed. These are the same methods that would be employed with data found on financial statements. He explained how to interpret the results.
In response to a question from a teleconference attendee on how to statistically evaluate a seasonal business, Williams advised splitting the financial data into “on” and “off” cycles and compare past years’ on cycles to each other and past years’ off cycles to each other. “Statistics can only help in apples to apples comparisons,” he said.
NACM teleconferences are an economical and convenient way to learn from the experts about the important topics many credit professionals must address. To find out about upcoming NACM audio teleconferences, go to NACM’s website at www.nacm.org. On the top of the page, place your cursor on the “Education” tab, then scroll down to “teleconferences.”
Source: Tom Diana, NACM staff writer


Determining the APR of that loan is easy. You merely require three figures: the total amount lent, the total finance cost, therefore the term amount of the mortgage.
To illustrate, letвЂ™s determine the APR for a $1,000 loan by having a $400 finance fee and a term that is 90-day.
- Divide the finance fee ($400) by the mortgage quantity ($1,000)
- Increase the effect (0.4) by the amount of times in the season (365)
- Divide the sum total (146) because of the word regarding the loan in days (90)
- Grow the total result(1.622) by 100 and include a portion indication
$400 / $1,000 x 365 /90 x 100 = 162.2%.
Effortless. But, determining the finance fee of that loan can get only a little more complex.
This calculator provides you with a concept exactly exactly just what interest levels and monthly premiums you can get centered on your credit rating, loan quantity, and term.


The Firing Squad Problem (FSP) is about designing a 1D cellular automaton, with n possible states for each cell, such that all cells will end up in the same state, having never been in that state before. Each cell follows the same set of rules (the "automaton"), which take the previous state of itself and its two neighbors, and outputs the next state for that cell. For cells at the edge, their neighbor is a special "null" state, which does not count to n.
A 6-state solution exists for all possible widths. It has been proven that there is no single 4-state solution for all possible widths, although 4-state solutions exist for powers of 2. It is unknown whether there is a single 5-state solution that works for all widths.


Probabilisitic estimation of uncertainties for 2D and 3D refraction seismic tomographic models
The goal of this project is to improve the efficiency of fully non-linear Markov chain Monte Carlo methods to obtain quantitative estimates of uncertainty for the inverted model parameters. We investigate the potential of multi-variate perturbations obtained propagating a random perturbation through the Resolution matrix. The project is funded by FWF.
Duration: 9/2011 - 8/2016
Personnel: C. Tauchner, BSc


What is a Satoshi? Each bitcoin (BTC) is divisible to the 8th decimal place, so each BTC can be split into 100,000,000 units. Each unit of bitcoin, or 0.00000001 bitcoin, is called a satoshi. A Satoshi is the smallest unit of Bitcoin. How many Satoshis are in a Bitcoin? There are 100,000,000 satoshi in a BTC.
The satoshi is currently the smallest unit of the bitcoin currency recorded on the block chain. It is a one hundred millionth of a single bitcoin (0.00000001 BTC).  The unit has been named in collective homage to the original creator of Bitcoin, Satoshi Nakamoto .
Oct 20, 2018 · A Satoshi is a one hundred millionth of a Bitcoin (0.00000001) and is currently the smallest unit of Bitcoin. 1 Satoshi is equal to 0.00000001 BTC 1 Bitcoin (BTC) = 100,000,000 Satoshis …
Each unit of bitcoin, or 0.00000001 bitcoin, is called a satoshi. A Satoshi is the smallest unit of Bitcoin. 1 Satoshi equals $ 0.0000000000 United States Dollar. Why is USD used to calculate satoshis value? Most BTC is traded in USD, so that is also a popular way to calculate satoshis value. Latest News on Bitcoin
1 bit = 1 microbitcoin = 1 μBTC = 0.000001 bitcoin (BTC) The term “bit” is a unit being used to represent smaller Bitcoin amounts. Due to the rising value of 1 bitcoin (currently 1 BTC = $7,884), many prices must be displayed in fractional bitcoin amounts.
What is a satoshi? Each bitcoin (1 BTC) can have a fractional part of up to 8 digits so 1 bitcoin can be divided into 100 000 000 units. Each of these bitcoin units (0.00000001 BTC) is called a satoshi. A satoshi is the smallest unit in a bitcoin. This unit is named after Satoshi Nakamoto – the alias of the bitcoin …
A bitcoin faucet is a website that is giving away free bitcoins to its registered users. To be able to claim all you have to do is to sign up on the website, solve a captcha and get free bitcoins. Here on Satoshi Hero once you reach 30 000 satoshi (0.0003 BTC), you’ll be able to withdraw the bitcoins to the address you’ve used during sign up.
Bitcoin Satoshi => USD. You can now select between which ticker to use above- Coindesk or BitcoinAverage Satoshi = USD $ 0 *Click the Satoshi value or USD value to change it* $ USD = x Satoshi = x BTC. BTC ฿1 = $ x USD. Refresh ↻ – occurs every 100 seconds … 1 Satoshi = 0.00000001 ฿ 10 Satoshi …
5 Answers. A Satoshi is a one hundred millionth of a Bitcoin. Bitcoins are delimited to eight decimal places so even if Bitcoins are worth $1,000,000 each, you can still do penny transactions.
100,000,000 Satoshi: 1.00000000 : 1 Bitcoin – BTC: O que é um Satoshi? Um Satoshi é a unidade mais pequena de Bitcoin, cada Bitcoin é divisível até a 8ª casa decimal, então cada Bitcoin pode ser dividido em 100.000.000 de unidades. Cada unidade de bitcoin, ou 0,00000001 bitcoin, é um Satoshi.


Clark County R-1 7th and 8th grade students, under the direction of Susan Turpin, competed in the Northeast Missouri Regional Professional Development Committee online math competition. On the first day of the contest local students led 16 schools to become the first daily winner. After six days, 51 Clark County students swarmed the competition to win first place overall. We are most proud of the following students placing in the top 10 out of 871 students: Mackenzie Arnold 1st, Blain Lindsey 7th, Karcyn McKee 8th,and Robin Cooksey 9th. Another 18 students from CCR-1 Middle School placed in the top 50 of the entire competition.
The competition is part of a software program entitled Sumdog. The students compete in mathematical games such as Junk Pile and Street Racing. Correct answers and speed of the computation determine the rankings. Our school received recognition as well as subscriptions for 30 students and a deluxe version of Junk Pile software for all Clark County R-1 participants.
Mrs Turpin says its exciting to see students working in their free time at school and home to review and drill math and computer skills. Mrs Yancy has now enrolled her students and we can set up grade level contests as well as students playing against their classmates.


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Maths – Recommended Books
These books were used by the blogger himself to Rank -110 in SSC CGL 2015 and Rank – 121 in SSC CGL 2016. Books for SSC Maths preparation is given below.
|1||Fast Track Objective Arithmetic|
|2||Quantum Aptitude Quantum CAT by Sarvesh K. Verma||Due to the increased difficulty level seen in SSC CGL 2017 Tier 2 Exam it is very important to get your concepts clear and practice slightly difficult Questions from this book.|
|3||Kiran’s SSC Mathematics 8900+|
For English Preparation Books: Click Here
Buy UPSC IAS Civil Service Study Material at Notes Clues : Click Here


One of the top technical institute in south India, International Institute of Information Technology, Bangalore has invited applications for MTech, MS and PhD courses in engineering for the academic year of 2013.
MTech will be two types. Integrated MTech and MTech
Eligibility conditions for integrated MTech: Candidates should have 10+2 with mathematics , candidates currently studying for 10+2 also can apply, but should be acquired the minimum qualification by Aug 2013.
Eligibility conditions for MTech: Minimum 60% marks in 12th and first-class four-year bachelor's degree in engineering (i.e. BE, BTech, or equivalent).
60% marks in 12th, degree and post graduate courses in any of the physical sciences or MCA degree. Final-year students expecting to graduate by August 2013 may also apply.
MS by Research: first-class four-year bachelor's degree in engineering (i.e. BE, BTech, or equivalent). MSc / MCA degree holders can also apply. Final-year students expecting to graduate by August 2013 may also apply.Out standing international candidates can also apply
PhD: First class four-year degree in a technical discipline (BE, BTech, or equivalent), but people holding 1st class Master's degrees in the mathematical sciences (e.g. an MSc in mathematics, physics, statistics, or electronics) may also apply. First class post graduate degree in technical discipline (MTech, ME) will be preferred
How to apply : apply online though IIIT website.
Application fee : Rs.1000/-
IIIT Bangalore MTech-MS and PhD admission 2013 Reviewed by traveller on 21.1.13 Rating:


|The Odd and Even Cha Cha|
Also included is a practice sheet that I use in guided math rotations (and double dip by using it as a formative assessment to add to my grade book!) and all the fixings for a differentiated file folder game. I hope y'all will take the time to check it out and see if it is something that your kids would enjoy as much as mine do! I'm not kidding when I say that all year my kids refer back to the odd and even cha cha song when helping to solve more advanced problems having to do with "fair share."
Hope you enjoy and HAPPY FRIDAY!!


In this constantly updated buying guide, we will help you choose the best scientific calculator that suits your needs. Will analyze all the characteristics and aspects to be considered when buying a product of this kind.
Is your university career starting, and have you decided to enroll in Engineering, Physics, or another scientific faculty? Then it’s good to retire your old calculator and buy a new model with interesting and useful features that will surely help you.
Table of Contents
How to choose a scientific calculator
Traditional calculators are valuable tools and are an integral part of a student’s life. However, you may have to perform more complicated calculations or study the graph of a function on the fly. And this is precisely where scientific models come into play.
Choosing a new scientific calculator isn’t as simple as it might seem. There are some features and some fundamental aspects to consider when buying. Only after a careful evaluation of the various features can you choose the perfect model for your needs.
Functions and Capabilities
Calculators differ from each other, mainly in size and built-in functionality. For this reason, it is good that you know immediately which operations you are going to perform most frequently.
Scientific calculators are capable of solving equations, derivatives, integrals, statistical calculations, and much more. However, some differ in the possibility of managing tables and graphics as well. Furthermore, it is good to opt for a model that allows you to easily switch between the various notations.
Some models allow you to connect to your computer to be able to pass python files or scripts. Of course, these are complex products that require some awareness and knowledge on the user’s part.
The size of the display also distinguishes scientific calculators. The display is a fundamental factor in choosing a product of this type. A good display quality simplifies and improves its use.
The display’s size is related to the complexity of the functions that the calculator can perform. For example, a high-end product can boast a high-resolution display that allows you to reproduce and animate various function graphics.
Obviously, the features of each calculator vary by price. For example, a budget model can perform 100-150 functions, while the high-end models, in addition to having a better and larger display, can perform over 500 different functions.
Each model has different memory sizes. Some are capable of storing even several GB of data. If you are an engineering, math, or physics student, we recommend purchasing a large storage space model.
The best scientific calculators chose by us
TEXAS INSTRUMENTS Instruments GRAFIKRECHNER TI-NSPIRE CX-II T CAS
This Texas Instrument jewel is a real miniature computer. The CX II-T CAS is equipped with a color display to draw and animate function graphs. The exact arithmetic function keeps the simplified functions’ mathematical structure, and the mathematical constants are recognized and symbolically simplified. In addition, the deSolve wizard allows you to minimize syntax errors in differential equations.
Also, it features support for the Python programming language. If you buy it from Amazon, you will get a free protective case and 5 years warranty.
ASIO PRIZM FX-CG50
It is undoubtedly one of the best scientific calculators currently available on the market. The display has 65,000 colors and allows you to take advantage of the Picture Plot functionality. In addition, of course, it allows you to solve equations, systems, differential equations, integrals, and much more.
This calculator also allows you to create 3D pie, bar, 3D charts with 7 different colors. Although it is a professional calculator, it is still admitted to the final exams.
NumWorks graphing calculator
Are you looking for a graphical, minimal, and affordable calculator? Then this NumWorks model is the product for you. A graphing calculator allows you to draw function graphs thanks to the high-resolution display (320 x 240 pixels). Its simplicity of use is its strong point.
You will be able to solve differential equations, integrals, and statistical calculations with great ease. Finally, it comes with Python support and has an extensive library of math, cmath, matplotlib.pyplot, turtle, and random.
This model can work with real numbers, complex numbers, vectors, and 4 × 4 matrices. It can perform integrals, derivatives, polynomial equations, and even linear systems of maximum size 4 × 4. Also, it comes with a built-in spreadsheet for up to 170 data. Thanks to the QR code reader, you can safely continue the calculations on your computer.
Finally, it is equipped with a dual solar and battery power supply.
Casio Fx-570Es Plus 2 Scientific Calculator
It is a cheap calculator, but it does its job very well. This CASIO template allows you to enter and view fractions and square roots just as they appear in your textbook. In addition, it can solve integrals and matrices with a maximum size of 4 × 4. It also allows you to convert polar coordinates into rectangular coordinates and vice versa.
The best-selling scientific calculators of the moment
Before concluding, we advise you to consult the following list of the 10 best-selling scientific calculators of the moment on Amazon. The list is kept constantly updated by the store itself.
Product prices and availability are subject to change. Any price and availablility information displayed on Amazon at the time of purchase will apply to the purchase of any products.