Foreword
Acknowledgments
Introduction
Chapter 1: Computers and Numbers
Optimize storage, perform arithmetic operations, and prevent overflow or precision errors
Chapter 2: Sets and Abstract Algebra
Data structures, cryptography, error detection and correction, and algorithm design
Chapter 3: Boolean Algebra
Logic gates as well as conditional statement, control structure, and algorithm development
Chapter 4: Functions and Relations
Define algorithms, understand dependencies between data, and design software components
Chapter 5: Induction
Prove algorithm correctness, particularly those that involve recursion or iterative processes
Chapter 6: Recurrence and Recursion
Algorithm performance and problem-solving
Chapter 7: Number Theory
Cryptography, hash functions, and efficient algorithm development
Chapter 8: Counting and Combinatorics
Analyze algorithm complexity and resource allocation, and solve permutation and probability problems
Chapter 9: Graphs
Network design, route optimization, connectivity solutions, and model relationships
Chapter 10: Trees
Essential for efficient searching, sorting, and parsing operations
Chapter 11: Probability
Model uncertainty, manage risk, and develop algorithms for randomized processes
Chapter 12: Statistics
Data analysis, model validation, decision-making, and machine learning algorithm development
Chapter 13: Linear Algebra
Computer graphics algorithms, machine learning models, and scientific computations
Chapter 14: Differential Calculus
Optimize functions, model change, and develop ML algorithms for training models
Chapter 15: Integral Calculus
Compute areas under curves, solve differential equations, and model continuous processes
Chapter 16: Differential Equations
Model and solve problems related to change and dynamic systems
Index

 Every great programming challenge has mathematical principles at its heart. Whether you’re optimizing search algorithms, building physics engines for games, or training neural networks, success depends on your grasp of core mathematical concepts.

 In Math for Programming, you’ll master the essential mathematics that will take you from basic coding to serious software development. You’ll discover how vectors and matrices give you the power to handle complex data, how calculus drives optimization and machine learning, and how graph theory leads to advanced search algorithms.

 Through clear explanations and practical examples, you’ll learn to:

• Harness linear algebra to manipulate data with unprecedented efficiency

• Apply calculus concepts to optimize algorithms and drive simulations

• Use probability and statistics to model uncertainty and analyze data

• Master the discrete mathematics that powers modern data structures

• Solve dynamic problems through differential equations

 Whether you’re seeking to fill gaps in your mathematical foundation or looking to refresh your understanding of core concepts, Math for Programming will turn complex math into a practical tool you’ll use every day.