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# Discrete Mathematics I

Course Code: MATH 1130
Faculty: Science & Technology
Department: Mathematics
Credits: 3.0
Semester: 15 weeks
Learning Format: Lecture, Tutorial
Typically Offered: Fall, Winter
course overview

This is the first of two Discrete Mathematics courses for Computing Science students. Topics include logic, set theory, functions, algorithms, mathematical reasoning, recursive definitions, counting and relations.

### Course Content

1. Logic
2. Set Theory
3. Functions
4. Algorithms, Integers and Matrices
5. Mathematical Reasoning and Recursive Definitions
6. Counting
7. Relations

Optional Topics

1. Graphs and Trees
2. Languages and Finite State Machines

### Methods of Instruction

Lectures, problem sessions, tutorial sessions and assignments

### Means of Assessment

Evaluation will be carried out in accordance with Douglas College policy.  The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester.  Evaluation will be based on some of the following:

 Weekly tests 0-40% Mid-term tests 20-70% Assignments 0-15% Attendance 0-5% Class participation 0-5% Tutorials 0-10% Final examination 30-40%

### Learning Outcomes

At the end of the course, the successful student should be able to:

• write English statements in symbolic form using prepositional variables or functions, logical connectives and any necessary quantifiers;
• determine the truth value of a statement under an interpretation;
• determine the negation, converse, inverse, and contrapositive of a statement;
• verify logical equivalencies;
• demonstrate an understanding of tautologies, contradictions and duals;
• prove the properties of logic;
• determine the cardinality of sets, subsets, power sets and Cartesian products;
• combine sets using the set operators;
• prove set identities using a series of known set identities or by showing that each expression is a subset of the other;
• use membership tables or Venn diagrams to prove set identities;
• classify functions as injective, surjective or bijective;
• demonstrate an understanding of domains, codomains, ranges, mappings and images;
• create new functions by composition;
• find the inverse of an injective function;
• demonstrate an understanding of the floor and ceiling functions;
• compute finite sums;
• give a big-O estimate for a function;
• write a simple algorithm in pseudocode;
• determine the time complexity of simple algorithms;
• demonstrate an understanding of divisibility, the greatest common divisor and modular arithmetic;
• use the Euclidean algorithm to find the gcd of two numbers;
• convert between binary, octal and hexadecimal;
• demonstrate an understanding of the rules of inference;
• analyze an argument as to its validity using the concepts of mathematical logic;
• use a direct proof, indirect proof, or contradiction to prove a mathematical theorem;
• prove mathematical theorems using formal inductive techniques;
• give a recursive definition of a function or a set;
• use the sum and product rules and tree diagrams to solve basic counting problems;
• apply the inclusion-exclusion principle to solve counting problems for two tasks;
• solve counting problems using the Pigeon-Hole Principle;
• count unordered selections of distinct objects;
• count ordered arrangements of a set of disctinct objects;
• count ordered and unordered selections of r objects chosen with or without repetition from a set of elements;
• count the number of arrangements of a set of objects some of which are indistinguishable;
• find the expansion of a binomial;
• determine the probability of a combination of events for an equi-probable sample space;
• determine whether or not a relation is reflexive, irreflexive, symmetric, antisymmetric and or transitive;
• represent a relation as a matrix and a digraph;

Optional Topics:

• determine whether a string belongs to the language generated by a given grammar;
• classify a grammar;
• find the language created by a grammar;
• draw the state diagram for a finite-state machine;
• construct a finite-state machine to perform a function;
• determine the output of a finite state machine;
• demonstrate an understanding of the vocabulary of graph theory;
• determine whether a graph is bi-partite or not;
• represent a graph as an adjacency matrix and an incidence matrix;
• determine whether a pair of graphs are isomorphic;
• find circuits and paths in a graph;

course prerequisites

Precalculus 12 with a C or better; or Foundations of Math 12 with a C or better.

curriculum guidelines

Course Guidelines for previous years are viewable by selecting the version desired. If you took this course and do not see a listing for the starting semester/year of the course, consider the previous version as the applicable version.

course schedule and availability
course transferability

Below shows how this course and its credits transfer within the BC transfer system.

A course is considered university-transferable (UT) if it transfers to at least one of the five research universities in British Columbia: University of British Columbia; University of British Columbia-Okanagan; Simon Fraser University; University of Victoria; and the University of Northern British Columbia.

For more information on transfer visit the BC Transfer Guide and BCCAT websites.

assessments

If your course prerequisites indicate that you need an assessment, please see our Assessment page for more information.