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Artemy Biryukov
Artemy Biryukov

Mathematica Tutorial: Mathematics And Algorithms


SciPy is a collection of mathematical algorithms and conveniencefunctions built on the NumPy extension of Python. It addssignificant power to the interactive Python session by providing theuser with high-level commands and classes for manipulating andvisualizing data. With SciPy, an interactive Python sessionbecomes a data-processing and system-prototyping environment rivalingsystems, such as MATLAB, IDL, Octave, R-Lab, and SciLab.




Mathematica Tutorial: Mathematics And Algorithms



Course description: This course introduces fundamental matrices and matrix algorithms used in applied mathematics, and essential theorems and their proofs. It covers matrices used in linear optimization, solving systems of linear differential equations, and modeling of stochastic processes. It also covers implementing matrix algorithms with mathematical software.


A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials.


GAP is a system for computational discrete algebra, with particularemphasis onComputational Group Theory.GAP provides a programming language, a library of thousands of functionsimplementing algebraic algorithms written in the GAP language as well aslargedata libraries ofalgebraic objects. See also theoverview andthe description of themathematical capabilities.GAP is used in research and teaching for studying groups and theirrepresentations, rings, vector spaces, algebras, combinatorialstructures, and more. The system, including source, is distributedfreely.You can study and easily modify or extend it for your special use.


Many mathematical topics are related to MATLAB that you can study, including trigonometry, linear algebra, interpolation, differential equations, graphs, network algorithms, and computational geometry. Graphics topics like two- and three-dimensional plots, animation, and images are also related to MATLAB. You can learn more about programming to enhance your study of MATLAB as well as app-building and software development. You can also study other programming languages, such as Java, C, C++, PHP, Python, and ASP since MATLAB can easily interact with other programs written in these languages.


Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.


Also, it seems like a lot of the responses here are from people who don't do mathematics, or who haven't used the languages they're suggesting to do mathematical software. The reason people recommend Haskell is because it's as close to a literal implementation of category theory as possible, and fits well with some mathematical definitions of some basic concepts. But if your friend is close to your age, then he is not ready for category theory mathematically (that maturity is more or less useless until graduate school, and wicked hard to teach yourself), and as a first language Haskell has the steepest learning curve of the languages suggested (perhaps Prolog is steeper). I used Haskell to implement a Javascript compiler, and I ended up with a very beautiful elegant piece of code, but for intuitive things like variable mutation, you already have to dabble in nontrivial monads.


One of the greatest motivating forces for Donald Knuth when he began developing the original TeX system was to create something that allowed simple construction of mathematical formulae, while looking professional when printed. The fact that he succeeded was most probably why TeX (and later on, LaTeX) became so popular within the scientific community. Typesetting mathematics is one of LaTeX's greatest strengths. It is also a large topic due to the existence of so much mathematical notation.


There are two noticeable problems: there are no spaces between words or numbers, and the letters are italicized and more spaced out than normal. Both issues are simply artifacts of the maths mode, in that it treats it as a mathematical expression: spaces are ignored (LaTeX spaces mathematics according to its own rules), and each character is a separate element (so are not positioned as closely as normal text).


The AMS (American Mathematical Society) mathematics package is a powerful package that creates a higher layer of abstraction over mathematical LaTeX language; if you use it it will make your life easier. Some commands amsmath introduces will make other plain LaTeX commands obsolete: in order to keep consistency in the final output you'd better use amsmath commands whenever possible. If you do so, you will get an elegant output without worrying about alignment and other details, keeping your source code readable. If you want to use it, you have to add this in the preamble: 041b061a72


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