Mathematics for Computer Scientists by Gareth J. Janacek, Mark Lemmon Close & Ventus Publishing ApS

mathematics-computer-scientThe aim of this book is to present some the basic mathematics that is needed by computer scientists. The reader is not expected to be a mathematician and the authors hope will find what follows useful. Just a word of warning, unless you are one of the irritating minority mathematics is hard. You cannot just read a mathematics book like a novel. The combination of the compression made by the symbols used and the precision of the argument make this impossible. It takes time and effort to decipher the mathematics and understand the meaning. It is a little like programming, it takes time to understand a lot of code and you never understand how to write code by just reading a manual – you have to do it, Mathematics is exactly the same, you need to do it. In this book the readers will read Numbers, Integers, Factors and primes, Modular arithmetic, The Euclidean algorithm, Rational and reals, Notation, Number systems, Addition in binary, Multiplication in decimal, Multiplication in binary, Octal, Hexadecimal.

 

The statement calculus and logic, Negation, Conjunction, Disjunction, The Bi-conditional, Arguments, Analyzing arguments using truth tables, Normal forms, Contradiction and consistency, Mathematical induction, Sets, Venn Diagrams and manipulating sets, Union, Cartesian product, Relations and functions, Counting, Chains of actions, Permutations, Combinations, Binomial expansions, Functions, The power function, Logarithms, Functions and angular measure, The trigonometric functions, Sequences, Bounded, Series, Infinite series, Absolute convergence, Alternating sign test,  Calculus, Continuity and differentiability, Higher derivatives, Maxima and minima, The Taylor expansion, Newton-Raphson method,  Algebra: Matrices, Vectors etc, Equation solving, Addition and subtraction, Multiplication by a scalar, Transpose of a matrix, Multiplication of matrices, Inverses, Geometry, Conditional probability, Looking at Data and much more.

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