This page covers the
following topics related to Discrete Mathematics : Logic and Sets, Relations and
Functions, the Natural Numbers, Division and Factorization , Languages, Finite
State Machines, Finite State Automata, Turing Machines, Groups and Modulo
Arithmetic, Introduction to Coding Theory, Group Codes, Public Key Cryptography,
Principle of Inclusion-exclusion, Generating Functions, Number of Solutions of a
Linear Equation, Recurrence Relations, Graphs, Weighted Graphs, Search
Algorithms, Digraphs.
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.
The aim of this note is to introduce fundamental concepts and
techniques in set theory in preparation for its many applications in computer science. Topics covered includes: Mathematical
argument, Sets and Logic, Relations and functions, Constructions on
sets, Well-founded induction.
This note
explains the following topics: Induction and Recursion, Steiner’s Problem,
Boolean Algebra, Set Theory, Arithmetic, Principles of Counting, Graph Theory.
This note explains the
following topics: positional and modular number systems, relations and their
graphs, discrete functions, set theory, propositional and predicate logic,
sequences, summations, mathematical induction and proofs by contradiction.
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 note
explains the following topics: Arithmetic, Logic and Numbers, Boolean Functions
and Computer Arithmetic, Number Theory and Cryptography, Sets, Equivalence and
Order, Functions, Induction, Sequences and Series, Lists, Decisions and Graphs,
Basic Counting and Listing, Decision Trees, Basic Concepts in Graph Theory.
Author(s): Edward A. Bender and S. Gill Williamson
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: Arithmetic, The Greatest Common Divisor, Subresultants, Modular
Techniques, Fundamental Theorem of Algebra, Roots of Polynomials, Sturm
Theory, Gaussian Lattice Reduction, Lattice Reduction and Applications,
Linear Systems, Elimination Theory, Groebner Bases, Bounds in Polynomial Ideal Theory and Continued
Fractions.