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kun j programmer rsquo s introduction mathematics 2018

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Textbook in PDF format A Programmer's Introduction to Mathematics uses your familiarity with ideas from programming and software to teach mathematics. You'll learn about the central objects and theorems of mathematics, including graphs, calculus, linear algebra, eigenvalues, optimization, and more. You'll also be immersed in the often unspoken cultural attitudes of mathematics, learning both how to read and write proofs while understanding why mathematics is the way it is. Between each technical chapter is an essay describing a different aspect of mathematical culture, and discussions of the insights and meta-insights that constitute mathematical intuition. As you learn, we'll use new mathematical ideas to create wondrous programs, from cryptographic schemes to neural networks to hyperbolic tessellations. Each chapter also contains a set of exercises that have you actively explore mathematical topics on your own. In short, this book will teach you to engage with mathematics. A Programmer's Introduction to Mathematics is written by Jeremy Kun, who has been writing about math and programming for 8 years on his blog "Math Intersect Programming." As of 2018, he works in datacenter optimization at Google. Our Goal Like Programming, Mathematics has a Culture Polynomials, Java, and Definitions A Little More Notation Existence & Uniqueness Realizing it in Code Application: Sharing Secrets Cultural Review Exercises Chapter Notes On Pace and Patience Sets Sets, Functions, and Their -Jections Clever Bijections and Counting Proof by Induction and Contradiction Application: Stable Marriages Cultural Review Exercises Chapter Notes Variable Names, Overloading, and Your Brain The Definition of a Graph Graph Coloring Register Allocation and Hardness Planarity and the Euler Characteristic Application: the Five Color Theorem Approximate Coloring Cultural Review Exercises Chapter Notes The Many Subcultures of Mathematics Calculus with One Variable Lines and Curves Limits The Derivative Taylor Series Remainders Application: Finding Roots Exercises On Types and Tail Calls Linear Algebra Linear Maps and Vector Spaces Linear Maps, Formally This Time The Basis and Linear Combinations Dimension Matrices Conjugations and Computations One Vector Space to Rule Them All Geometry of Vector Spaces Application: Singular Value Decomposition Exercises Chapter Notes Live and Learn Linear Algebra (Again) Eigenvectors and Eigenvalues Eigenvalues of Graphs Limiting the Scope: Symmetric Matrices Inner Products Orthonormal Bases Computing Eigenvalues The Spectral Theorem Application: Waves Cultural Review Exercises Chapter Notes Rigor and Formality Generalizing the Derivative Linear Approximations Multivariable Functions and the Chain Rule Computing the Total Derivative The Geometry of the Gradient Optimizing Multivariable Functions The Chain Rule: a Reprise and a Proof Gradient Descent: an Optimization Hammer Gradients of Computation Graphs Application: Automatic Differentiation and a Simple Neural Network Exercises Chapter Notes The Argument for Big-O Notation Groups The Geometric Perspective The Interface Perspective Homomorphisms: Structure Preserving Functions Building Blocks of Groups Geometry as the Study of Groups The Symmetry Group of the Poincaré Disk The Hyperbolic Isometry Group as a Group of Matrices Application: Drawing Hyperbolic Tessellations Exercises Chapter Notes A New Interface About the Author and Cover Index

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Details for: Kun J. A Programmer’s Introduction to Mathematics 2018

kun j programmer rsquo s introduction mathematics 2018

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Details for: Kun J. A Programmer&rsquo;s Introduction to Mathematics 2018

kun j programmer rsquo s introduction mathematics 2018

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Details for: Kun J. A Programmer’s Introduction to Mathematics 2018