CHAPTER 1 5Introduction To Mathematics For Computing 7Definitions 8Mathematical Foundations 9Basic Mathematical Concepts for Computing 11Foundations of Mathematical Structures in Computing 13Sets 13Set Operations 14Subsets and power sets 14Cartesian product of sets 15Sequences and Series 15Definition of sequences 16Arithmetic and geometric sequences 17Series and convergence 18Functions 18Function notation and domain and range 19Types of functions: injective, surjective, and bijective 20Composition of functions 21Inverse functions 22Binary Relations 22Properties of relations 24Equivalence relations and partitions 25Partial order relations 26Logical Foundations of Mathematics for Computing 27Propositions, Predicates, and Axiomatic Method 27Proving an Implication and "If and Only If" 28Proof by Cases and Contradiction 29Number theory 30Divisibility 31Prime numbers 32Modular arithmetic 33Chapter 1 Exercises and More 34Practice questions 34Key takeaways 34Answers to the practice questions 35Project work 37Projet help 37Mathematical symbols and notations 38Revisions (Flashcard topics) 38CHAPTER 2 41Discrete Mathematics And Algorithms 43Set Theory 44Sets, subsets, and power sets 44Set operations (union, intersection, difference, complement) 44Venn diagrams and set identities 45Cartesian product of sets 45Countable and uncountable sets 46Logic and Propositional Calculus 47Propositions and logical connectives 47Logical equivalence and logical implications 48Tautologies and contradictions 48Rules of inference and proof techniques 48Quantifiers (universal and existential) 49Combinatorics and Counting Principles 50Combinatorics 50Permutations and combinations 51The pigeonhole principle 52Binomial coefficients 52Inclusion-exclusion principle 53Graph Theory 54Graphs, vertices, and edges 55Graph representations 55Types of Graphs 56Graph representations 58Graph properties 59Graph algorithms 59Discrete Probability 61Sample spaces and events 61Probability rules and axioms 61Conditional probability and independence 61Bayes' theorem 62Random variables and probability distributions 62Recursion and Recurrence Relations 64Recursive algorithms and functions 64Recurrence relations and their solutions 64Master theorem for solving recurrences 65Generating functions for solving recurrences 65Number Theory 66Divisibility and modular arithmetic 66GCD and LCM 66Prime numbers and factorisation 66Diophantine.