University of Cambridge's "Information Theory, Inference, and Learning Algorithms" by David J. C. MacKay Free, author-released full book (628 pages), with Cambridge University Press's permission. PDF: inference.org.uk/itprnn/book… Book site: inference.org.uk/mackay/itil…

A fantastic textbook "Discrete Mathematics: An Open Introduction" (3rd edition) by Oscar Levin (2025) is now in @ChapterPal's collection. The book Introduces fundamental concepts in discrete mathematics through interactive problems in counting, sequences, symbolic logic, and graph theory. The book has 120 figures and 510 exercises, most of which are interactive with feedback. Read the book with an AI tutor: chapterpal.com/book/1cd4b139… Chapter 0: Introduction and Preliminaries ## 0.1 What is Discrete Mathematics? ## 0.2 Mathematical Statements ### Atomic and Molecular Statements ### Implications ### Exercises ## 0.3 Sets ### Notation ### Relationships Between Sets ## 0.4 Functions ### Describing Functions ### Image and Inverse Image Chapter 1: Counting ## 1.1 Additive and Multiplicative Principles ### Principle of Inclusion/Exclusion ### Exercises ### Subsets ### Bit Strings ### Lattice Paths ### Binomial Coefficients ### Pascal’s Triangle ### Exercises ## 1.3 Combinations and Permutations ## 1.4 Combinatorial Proofs ### Patterns in Pascal’s Triangle ### Exercises ## 1.6 Advanced Counting Using PIE ## 1.7 Chapter Summary ### Chapter Review Chapter 2: Sequences ## 2.1 Describing Sequences ### Sums of Arithmetic and Geometric Sequences ## 2.3 Polynomial Fitting ## 2.4 Solving Recurrence Relations ## 2.5 Induction ### Stamps ### Formalizing Proofs ### Examples ### Strong Induction ### Exercises ### Chapter Review Chapter 3: Symbolic Logic and Proofs ## 3.1 Propositional Logic ### Truth Tables ## 3.2 Proofs ### Direct Proof ### Proof by Contrapositive ### Proof by Contradiction ### Proof by (counter) Example ### Exercises ## 3.3 Chapter Summary ### Chapter Review Chapter 4: Graph Theory ### Named Graphs. ### Graph Theory Definitions. ### Exercises ### Properties of Trees ### Rooted Trees ### Non-planar Graphs ### Polyhedra ### Exercises ### Coloring in General ### Coloring Edges ### Exercises ### Hamilton Paths ## 4.6 Matching in Bipartite Graphs ## 4.7 Chapter Summary ### Chapter Review Chapter 5: Additional Topics ## 5.1 Generating Functions ### Differencing ## 5.2 Introduction to Number Theory ### Divisibility ### Remainder Classes ### Properties of Congruence ### Solving Linear Diophantine Equations