The goal of this lecture note is to introduce students to ideas and
techniques from discrete mathematics that are widely used in Computer
Science. This note covers the following topics: Propositional logic,
Induction, Strong induction, Structural induction, Proofs about algorithms,
Algebraic algorithms, Number theory, RSA, Basics of counting, basic
probability,Conditional probability, Linearity of expectation, variance.
This note explains the following topics related to Discrete
Mathematics : Mathematical Logic, Relations, Algebraic structures,
Elementary Combinatorics, Recurrence Relation, Graph Theory.
Author(s): Malla Reddy College Of Engineering
and Technology
This PDF covers the following topics related to Discrete
Mathematics : Introduction, Sets, Functions, Counting, Relations, Sequences,
Modular Arithmetic, Asymptotic Notation, Orders.
Author(s): Andrew D. Ker, Oxford University Computing
Laboratory
This PDF covers the following
topics related to Discrete Mathematics : Introduction, Propositional Logic,
Sets, and Induction, Relations, Functions, Counting, Sequences, Graphs and
trees, A glimpse of infinity.
This note
explains the following topics: Induction and Recursion, Steiner’s Problem,
Boolean Algebra, Set Theory, Arithmetic, Principles of Counting, Graph Theory.
This
lecture note describes the following topics: Sets and Notation, Induction, Proof
Techniques, Divisibility, Prime Numbers, Modular Arithmetic, Relations and
Functions, Mathematical Logic, Counting, Binomial Coefficients, The
Inclusion-Exclusion Principle, The Pigeonhole Principle, Asymptotic Notation,
Graphs, Trees, Planar Graphs.
This
note covers the following topics: Logic, Asymptotic Notation, Convex Functions
and Jensen’s Inequality, Basic Number Theory, Counting, Binomial coefficients,
Graphs and Digraphs, Finite Probability Space, Finite Markov Chains.
This is a course
note on discrete mathematics as used in Computer Science. Topics covered
includes: Mathematical logic, Set theory, The real numbers, Induction and
recursion, Summation notation, Asymptotic notation, Number theory, Relations,
Graphs, Counting, Linear algebra, Finite fields.
This note
covers the following topics: Preliminaries, Counting and Permutations,
Advanced Counting, Polya Theory, Generating Functions and Its Applications.
This note
covers the following topics: induction, counting subsets, Pascal's triangle,
Fibonacci numbers, combinatorial probability, integers divisors and primes,
Graphs, Trees, Finding the optimum, Matchings in graphs, Graph coloring.
This note explains the following topics: Relations, Maps, Order
relations, Recursion and Induction, Bounding some recurrences, Graphs, Lattices
and Boolean Algebras.
This note covers the following topics:
Compound Statements, Sets and subsets, Partitions and counting,
Probability theory, Vectors and matrices, Linear programming and the
theory of games, Applications to behavioral science problems.
Author(s): John G. Kemeny, J. Laurie
Snell, and Gerald L. Thompson
This note covers the
following topics: Logic and Foundations, Proposition logic and
quantifiers, Set Theory, Mathematical Induction, Recursive Definitions,
Properties of Integers, Cardinality of Sets, Pigeonhole Principle,
Combinatorial Arguments, Recurrence Relations.
This
book explains the following topics: Computability, Initiation to Complexity Theory, The Turing Model: Basic
Results, Introduction to the Class NP, Reducibilities, Complete
Languages, Separation Results, Stochastic Choices, Quantum Complexity,
Theory of Real Computation and Kolmogorov Complexity.