Discrete Structures Lecture Notes by Vladlen Koltun
Discrete Structures Lecture Notes by Vladlen Koltun
Discrete Structures Lecture Notes by Vladlen Koltun
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.
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: 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 covers the following topics: Sets, Functions and Relations, Proofs
and Induction, Number Theory, Counting, Probability, Logic, Graphs, Finite
Automata.
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
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
covers the following topics: Preliminaries, Counting and Permutations,
Advanced Counting, Polya Theory, Generating Functions and Its Applications.
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 book consists of six units of study: Boolean Functions and
Computer Arithmetic, Logic, Number Theory and Cryptography, Sets and Functions,
Equivalence and Order, Induction, Sequences and Series. Each of this is divided into two sections.
Each section contains a representative selection of problems. These vary from
basic to more difficult, including proofs for study by mathematics students or
honors students.
Author(s): Edward A. Bender and S. Gill
Williamson
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.
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.