Mathematics for Algorithm and Systems Analysis

The second part of the two series of book, used to teach discrete mathematics that includes Boolean arithmetic, combinatorics, elementary logic, induction, graph theory and finite probability in the University of California, San Diego.

**Tag(s):**
Discrete Mathematics

**Publication date**: 01 Jul 2005

**ISBN-10**:
0486442500

**ISBN-13**:
n/a

**Paperback**:
248 pages

**Views**: 20,217

Mathematics for Algorithm and Systems Analysis

The second part of the two series of book, used to teach discrete mathematics that includes Boolean arithmetic, combinatorics, elementary logic, induction, graph theory and finite probability in the University of California, San Diego.

Book Excerpts:

Discrete mathematics is an essential tool in almost all subareas of computer science. Interesting and challenging problems in discrete mathematics arise in programming languages, computer architecture, networking, distributed systems, database systems, AI, theoretical computer science, and other areas.

This textbook is the second part of the two series of book, used to teach two-quarter course sequence in discrete mathematics that includes Boolean arithmetic, combinatorics, elementary logic, induction, graph theory and finite probability in the University of California, San Diego (USCD). These courses are core undergraduate requirements for majors in Computer Science, Computer Engineering, and Mathematics-Computer Science.

This text, Mathematics for Algorithm and System Analysis, was developed for the second quarter and the other text, A Short Course in Discrete Mathematics was developed for the first quarter. With appropriate students, this text could be used without the first.

This book consists of four units of study (Counting and Listing -- CL; Functions -- Fn; Decision Trees and Recursion -- DT; and Basic Concepts of Graph Theory -- GT), each divided into four 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. The first three sections in units CL and Fn are primarily a review of material in A Short Course in Discrete Mathematics needed for this course.

The review questions. 'Multiple Choice Questions for Review' appear at the end of each unit. The explanatory material in this book is directed towards giving students the mathematical language and sophistication to recognize and articulate the ideas behind these questions and to answer questions that are similar in concept and difficulty. Many variations of these questions have been successfully worked on exams by most beginning students using this book at UCSD.

Intended Audience:

Students who master the ideas and mathematical language needed to understand these review questions gain the ability to formulate, in the neutral language of mathematics, problems that arise in various applications of computer science. This skill greatly facilitates their ability to discuss problems in discrete mathematics with other computer scientists and with mathematicians.

Discrete mathematics is an essential tool in almost all subareas of computer science. Interesting and challenging problems in discrete mathematics arise in programming languages, computer architecture, networking, distributed systems, database systems, AI, theoretical computer science, and other areas.

This textbook is the second part of the two series of book, used to teach two-quarter course sequence in discrete mathematics that includes Boolean arithmetic, combinatorics, elementary logic, induction, graph theory and finite probability in the University of California, San Diego (USCD). These courses are core undergraduate requirements for majors in Computer Science, Computer Engineering, and Mathematics-Computer Science.

This text, Mathematics for Algorithm and System Analysis, was developed for the second quarter and the other text, A Short Course in Discrete Mathematics was developed for the first quarter. With appropriate students, this text could be used without the first.

This book consists of four units of study (Counting and Listing -- CL; Functions -- Fn; Decision Trees and Recursion -- DT; and Basic Concepts of Graph Theory -- GT), each divided into four 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. The first three sections in units CL and Fn are primarily a review of material in A Short Course in Discrete Mathematics needed for this course.

The review questions. 'Multiple Choice Questions for Review' appear at the end of each unit. The explanatory material in this book is directed towards giving students the mathematical language and sophistication to recognize and articulate the ideas behind these questions and to answer questions that are similar in concept and difficulty. Many variations of these questions have been successfully worked on exams by most beginning students using this book at UCSD.

Intended Audience:

Students who master the ideas and mathematical language needed to understand these review questions gain the ability to formulate, in the neutral language of mathematics, problems that arise in various applications of computer science. This skill greatly facilitates their ability to discuss problems in discrete mathematics with other computer scientists and with mathematicians.

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About The Author(s)

Edward A. Bender is a Professor Emeritus of Mathematics in the Department of Mathematics at the UC San Diego. He received his Ph.D. in Mathematics at California Institute of Technology in 1966.

S. Gill Williamson is Professor Emeritus in the Department of Computer Science and Engineering at the University of California San Diego. His main research area is Algorithmic Combinatorics.

Book Categories

Computer Science
16
Introduction to Computer Science
32
Introduction to Computer Programming
52
Algorithms and Data Structures
25
Artificial Intelligence
24
Computer Vision
31
Machine Learning
6
Neural Networks
22
Game Development and Multimedia
25
Data Communication and Networks
5
Coding Theory
16
Computer Security
9
Information Security
35
Cryptography
3
Information Theory
17
Computer Organization and Architecture
22
Operating Systems
2
Image Processing
11
Parallel Computing
4
Concurrent Programming
24
Relational Database
3
Document-oriented Database
14
Data Mining
17
Big Data
18
Data Science
23
Digital Libraries
22
Compiler Design and Construction
26
Functional Programming
13
Logic Programming
27
Object Oriented Programming
22
Formal Methods
71
Software Engineering
3
Agile Software Development
7
Information Systems
5
Geographic Information System (GIS)

Mathematics
68
Mathematics
14
Algebra
1
Abstract Algebra
27
Linear Algebra
3
Number Theory
8
Numerical Methods
2
Precalculus
10
Calculus
3
Differential Equations
5
Category Theory
11
Proofs
20
Discrete Mathematics
24
Theory of Computation
15
Graph Theory
2
Real Analysis
1
Complex Analysis
15
Probability
48
Statistics
7
Game Theory
5
Queueing Theory
13
Operations Research
16
Computer Aided Mathematics

Supporting Fields
21
Web Design and Development
1
Mobile App Design and Development
28
System Administration
2
Cloud Computing
12
Electric Circuits
7
Embedded System
28
Signal Processing
4
Network Science
3
Project Management

Operating System
Programming/Scripting
6
Ada
13
Assembly
34
C / C++
8
Common Lisp
2
Forth
35
Java
13
JavaScript
1
Lua
15
Microsoft .NET
1
Rexx
12
Perl
6
PHP
69
Python
12
R
1
Rebol
13
Ruby
2
Scheme
3
Tcl/Tk

Miscellaneous