دانلود کتاب A Programmer’s Introduction to Mathematics

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Contents
Our Goal i
Chapter 1. Like Programming, Mathematics has a Culture
Chapter 2. Polynomials
2.1 Polynomials, Java, and Definitions
2.2 A Little More Notation
2.3 Existence & Uniqueness
2.4 Realizing it in Code
2.5 Application: Sharing Secrets
2.6 Cultural Review
2.7 Exercises
2.8 Chapter Notes
Chapter 3. On Pace and Patience
Chapter 4. Sets
4.1 Sets, Functions, and Their -Jections
4.2 Clever Bijections and Counting
4.3 Proof by Induction and Contradiction
4.4 Application: Stable Marriages
4.5 Cultural Review
4.6 Exercises
4.7 Chapter Notes
Chapter 5. Variable Names, Overloading, and Your Brain
Chapter 6. Graphs
6.1 The Definition of a Graph
6.2 Graph Coloring
6.3 Register Allocation and Hardness
6.4 Planarity and the Euler Characteristic
6.5 Application: the Five Color Theorem
6.6 Approximate Coloring
6.7 Cultural Review
6.8 Exercises
6.9 Chapter Notes
Chapter 7. The Many Subcultures of Mathematics
Chapter 8. Calculus with One Variable
8.1 Lines and Curves
8.2 Limits
8.3 The Derivative
8.4 Taylor Series
8.5 Remainders
8.6 Application: Finding Roots
8.7 Cultural Review
8.8 Exercises
Chapter 9. On Types and Tail Calls
Chapter 10. Linear Algebra
10.1 Linear Maps and Vector Spaces
10.2 Linear Maps, Formally This Time
10.3 The Basis and Linear Combinations
10.4 Dimension
10.5 Matrices
10.6 Conjugations and Computations
10.7 One Vector Space to Rule Them All
10.8 Geometry of Vector Spaces
10.9 Application: Singular Value Decomposition
10.10 Cultural Review
10.11 Exercises
10.12 Chapter Notes
Chapter 11. Live and Learn Linear Algebra (Again)
Chapter 12. Eigenvectors and Eigenvalues
12.1 Eigenvalues of Graphs
12.2 Limiting the Scope: Symmetric Matrices
12.3 Inner Products
12.4 Orthonormal Bases
12.5 Computing Eigenvalues
12.6 The Spectral Theorem
12.7 Application: Waves
12.8 Cultural Review
12.9 Exercises
12.10 Chapter Notes
Chapter 13. Rigor and Formality
Chapter 14. Multivariable Calculus and Optimization
14.1 Generalizing the Derivative
14.2 Linear Approximations
14.3 Vector-valued Functions and the Chain Rule
14.4 Computing the Total Derivative
14.5 The Geometry of the Gradient
14.6 Optimizing Multivariable Functions
14.7 Gradient Descent: an Optimization Hammer
14.8 Gradients of Computation Graphs
14.9 Application: Automatic Differentiation and a Simple Neural Network
14.10 Cultural Review
14.11 Exercises
14.12 Chapter Notes
Chapter 15. The Argument for Big-O Notation
Chapter 16. Groups
16.1 The Geometric Perspective
16.2 The Interface Perspective
16.3 Homomorphisms: Structure Preserving Functions
16.4 Building Blocks of Groups
16.5 Geometry as the Study of Groups
16.6 The Symmetry Group of the Poincaré Disk
16.7 Application: Drawing Hyperbolic Tessellations
16.8 Cultural Review
16.9 Exercises
16.10 Chapter Notes
Chapter 17. A New Interface
Appendix A. Notation
Appendix B. A Summary of Proofs
B.1 Propositional and first-order logic
B.2 Methods of proof
B.3 How does one actually prove things?
Appendix C. Annotated Resources
C.1 Fundamentals and Foundations
C.2 Polynomials
C.3 Graph Theory and Combinatorics
C.4 Calculus and Analysis
C.5 Linear Algebra
C.6 Optimization
C.7 Abstract Algebra (Groups, etc.)
C.8 Topology
C.9 Computer Science, Theory, and Algorithms
C.10 Fun and Recreation
About the Author and Cover
Index