# View Descriptor

## Descriptor Details

• Discrete Math
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• 160
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• 3.0
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• Uploaded: 10/12/2017 04:44:05 PM PDT

## General Description

Fundamental topics for Computer Science, such as logic, proof techniques, sets, introduction to computer programming, basic counting rules, relations, functions and recursion, graphs and probability trees.

## Prerequisites

College Algebra for STEM (C-ID Math 151) or Precalculus (C-ID Math 155) or Precalculus and Trigonometry (sequence course)

## Content

1. Formal logic including statements, symbolic representation, tautologies, propositional logic, quantifiers, predicates, and validity, predicate logic, and logic programming;
2. Proofs, recursion, and analysis of algorithms including proof techniques, proof by induction, proof of correctness programming, recursive definitions, recurrence relations, and analysis of algorithms;
3. Sets, combinatorics, probability, and number theory including counting, principle of inclusion and exclusion; Pigeonhole Principle, permutations and combinations, and Binomial Theorem;
4. Relations, functions, and matrices including relations and databases, modular arithmetic;
5. Graphs and trees including graphs and their representations, trees and their representations, decision trees, and Huffman Codes;
6. Graph algorithms including directed graphs and binary relations; Warshall’s algorithm, Euler Path and Hamiltonian Circuit, shortest path and minimal spanning tree, traversal algorithms, and articulation points and computer networks;
7. Boolean Algebra and computer logic including Boolean algebra structure, logic networks, and minimization; and
8. Modeling arithmetic, computation, and languages including algebraic structures, finite-state machines, and formal languages.

## Objectives

Upon successful completion of the course, students will be able to:

1. Use recursion to analyze algorithms and programs;
2. Write proofs using symbolic logic and Boolean Algebra;
3. Use sets to solve problems in combinatorics and probability theory;
4. Apply matrices to analyze graphs and trees; and
5. Use finite state machines to model computer operations.

## Evaluation Methods

Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems.

## Textbooks

A college level textbook supporting the learning objectives of this course.

• No
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