# SRJC Course Outlines

 9/28/2023 1:53:57 AM MATH 4 Course Outline as of Fall 2021 Changed Course CATALOG INFORMATION Discipline and Nbr:  MATH 4 Title:  DISCRETE MATHEMATICS Full Title:  Discrete Mathematics Last Reviewed:9/14/2020

 Units Course Hours per Week Nbr of Weeks Course Hours Total Maximum 4.00 Lecture Scheduled 4.00 17.5 max. Lecture Scheduled 70.00 Minimum 4.00 Lab Scheduled 0 6 min. Lab Scheduled 0 Contact DHR 0 Contact DHR 0 Contact Total 4.00 Contact Total 70.00 Non-contact DHR 0 Non-contact DHR Total 0

 Total Out of Class Hours:  140.00 Total Student Learning Hours: 210.00

Title 5 Category:  AA Degree Applicable
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As:
Formerly:

Catalog Description:
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Introductory discrete mathematics course including formal logic, Boolean logic and logic circuits, mathematical induction, introduction to number theory, set theory, principles of combinatorics, functions, relations, recursion, algorithm efficiency and graph theory.

Prerequisites/Corequisites:
Completion of MATH 27 or higher (MATH); OR Course Completion of MATH 25 and MATH 58; OR AB705 placement into Math Tier 4

Recommended Preparation:
Course Completion of MATH 1A

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
Introductory discrete mathematics course including formal logic, Boolean logic and logic circuits, mathematical induction, introduction to number theory, set theory, principles of combinatorics, functions, relations, recursion, algorithm efficiency and graph theory.

Prerequisites:Completion of MATH 27 or higher (MATH); OR Course Completion of MATH 25 and MATH 58; OR AB705 placement into Math Tier 4
Recommended:Course Completion of MATH 1A
Limits on Enrollment:
Transfer Credit:CSU;UC.
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP

ARTICULATION, MAJOR, and CERTIFICATION INFORMATION

 Associate Degree: Effective: Fall 1981 Inactive: Area: BMC Communication and Analytical ThinkingMath Competency CSU GE: Transfer Area Effective: Inactive: B4 Math/Quantitative Reasoning Fall 2001 IGETC: Transfer Area Effective: Inactive: 2A Mathematical Concepts & Quantitative Reasoning Fall 2001 CSU Transfer: Transferable Effective: Fall 2001 Inactive: UC Transfer: Transferable Effective: Fall 2001 Inactive: C-ID:

Certificate/Major Applicable: Major Applicable Course

COURSE CONTENT

Student Learning Outcomes:
At the conclusion of this course, the student should be able to:
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1. Recognize valid forms of arguments using predicate logic.
2. Construct mathematical proofs of propositions from elementary number theory.
3. Apply combinatorics and set theory to counting problems.
4. Analyze formal languages using finite-state automata.

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At the conclusion of this course, the student should be able to:
1.   Properly structure mathematical algorithms and proofs.
2.   Prove theorems by induction.
3.   Apply algorithms from elementary number theory.
4.   Use set theory and Boolean algebra to construct and write proofs and solve problems.
5.   Apply combinatorics to counting problems, including use of Pigeonhole Principle, permutations, combinations, and probability.
6.   Analyze functions, inverse functions, and finite-state automata.
7.   Solve recurrence relations and use recursion to analyze algorithms and programs.
8.   Analyze the efficiency of algorithms.
9.   Recognize relations and their properties.
10. Use graph theory and matrix representations to develop appropriate models.
11. Apply matrices to analyze graphs and trees.

Topics and Scope
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I. Logic
A. Logical form, tautology, and symbolic representation in propositional logic
B. Equivalence and minimization of Boolean circuits
C. Valid and invalid arguments
D. Quantified statements and predicate logic
E. Proof strategies with number theory
F. Logic programming
II. Mathematical Induction
A. Sequences
B. Weak and strong induction
C. Well-ordering principle
D. Correctness of algorithms
III. Combinatorics
A. Counting
B. Probability
C. Possibility trees
D. Multiplication rule
F. Inclusion/exclusion
G. Permutations
H. Combinations and Binomial Theorem
I.  Counting of multisets
J. Pigeonhole Principle
IV. Set Theory
A. Definitions
B. Binary operations
C. Properties
D. Partitions
E. Power sets
V. Functions
A. Definition
B. One-to-one, onto, and inverse functions
C. Composition of functions
VI. Recursion
A. Sequences defined recursively
B. Solving recurrence relations by iteration
C. Solutions of second-order linear homogeneous recurrence relations with constant coefficients
VII. Algorithm Efficiency
A. Comparison of real valued functions and their graphs
B. Big O notation
C. Calculations of efficiency
VIII. Relations
A. Relations on sets
B. Reflexivity
C. Symmetry
D. Transitivity
E. Equivalence relations with number theory and modular arithmetic
F. Relational databases
G. Matrix representation
IX. Graph Theory
A. Paths, Euler and Hamiltonian paths and circuits
B. Matrix and visual representations of graphs
C. Representations of trees, diagrams
D. Trees and its applications: decision trees, Huffman codes
E. Graph algorithms, including directed graphs, binary relations, shortest path and minimal spanning tree, and Warshall's algorithm (minimal weighted paths)
F. Tree traversal algorithms
G. Articulation points (cut vertices) and computer networks
X. Boolean Algebra Structure
A. Logic networks
B. Minimization
XI. Formal Languages and Automata
A. Languages and regular expressions
B. Finite-state automata
C. Modeling arithmetic, computation, and languages including algebraic structures, formal languages

Assignments:
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1. Reading assignments (0-50 pages per week)
2. Homework assignments (15-30) consisting of 5-35 problems from required text(s) or supplementary materials chosen by the instructor
3. Quiz(zes) (0-8)
4. Exams (2-7)
5. Final Exam
6. Project(s) (0-2): research papers on a specific topic (5-10 pages) or presentations given as posters or short talks.Papers and presentations must be related to topics taught in the course.