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# Major Mathematics and Computer Science (72 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Science

### Program Requirements

#### Program Prerequisites

Students entering the Joint Major in Mathematics and Computer Science are normally expected to have completed the courses below or their equivalents. Otherwise, they will be required to make up any deficiencies in these courses over and above the 72 credits of courses in the program specification.

• MATH 133 Linear Algebra and Geometry (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Systems of linear equations, matrices, inverses, determinants; geometric vectors in three dimensions, dot product, cross product, lines and planes; introduction to vector spaces, linear dependence and independence, bases. Linear transformations. Eigenvalues and diagonalization.

Terms: Fall 2020, Winter 2021, Summer 2021

Instructors: Bélanger-Rioux, Rosalie; Ball, Gavin; Aigner, Florian; Przytycki, Piotr (Fall) Kelome, Djivede (Winter)

• 3 hours lecture, 1 hour tutorial

• Prerequisite: a course in functions

• Restriction A: Not open to students who have taken MATH 221 or CEGEP objective 00UQ or equivalent.

• Restriction B: Not open to students who have taken or are taking MATH 123, except by permission of the Department of Mathematics and Statistics.

• Restriction C: Not open to students who are taking or have taken MATH 134.

• MATH 140 Calculus 1 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.

Terms: Fall 2020, Winter 2021, Summer 2021

Instructors: Trudeau, Sidney; Ghaswala, Tyrone; Albanese, Michael (Fall) Fortier, Jérôme (Winter)

• 3 hours lecture, 1 hour tutorial

• Prerequisite: High School Calculus

• Restriction: Not open to students who have taken MATH 120, MATH 139 or CEGEP objective 00UN or equivalent

• Restriction: Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics

• Each Tutorial section is enrolment limited

• MATH 141 Calculus 2 (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.

Terms: Fall 2020, Winter 2021, Summer 2021

Instructors: Fortier, Jérôme; Sabok, Marcin (Fall) Trudeau, Sidney; Albanese, Michael; Ghaswala, Tyrone (Winter)

• Prerequisites: MATH 139 or MATH 140 or MATH 150.

• Restriction: Not open to students who have taken MATH 121 or CEGEP objective 00UP or equivalent

• Restriction Note B: Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics.

• Each Tutorial section is enrolment limited

#### Required Courses (54 credits)

* Students who have sufficient knowledge in a programming language do not need to take COMP 202 but can replace it with an additional Computer Science complementary course.

• COMP 202 Foundations of Programming (3 credits) *

Offered by: Computer Science (Faculty of Science)

### Overview

Computer Science (Sci) : Introduction to computer programming in a high level language: variables, expressions, primitive types, methods, conditionals, loops. Introduction to algorithms, data structures (arrays, strings), modular software design, libraries, file input/output, debugging, exception handling. Selected topics.

Terms: Fall 2020, Winter 2021

Instructors: Alberini, Giulia; Campbell, Jonathan (Fall) Alberini, Giulia; Campbell, Jonathan (Winter)

• 3 hours

• Prerequisite: a CEGEP level mathematics course

• Restrictions: COMP 202 and COMP 208 cannot both be taken for credit. COMP 202 is intended as a general introductory course, while COMP 208 is intended for students interested in scientific computation. COMP 202 cannot be taken for credit with or after COMP 250

• COMP 206 Introduction to Software Systems (3 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

Computer Science (Sci) : Comprehensive overview of programming in C, use of system calls and libraries, debugging and testing of code; use of developmental tools like make, version control systems.

Terms: Fall 2020, Winter 2021

Instructors: D'silva, Joseph (Fall) D'silva, Joseph; Vybihal, Joseph P (Winter)

• COMP 250 Introduction to Computer Science (3 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

Computer Science (Sci) : Mathematical tools (binary numbers, induction, recurrence relations, asymptotic complexity, establishing correctness of programs), Data structures (arrays, stacks, queues, linked lists, trees, binary trees, binary search trees, heaps, hash tables), Recursive and non-recursive algorithms (searching and sorting, tree and graph traversal). Abstract data types, inheritance. Selected topics.

Terms: Fall 2020, Winter 2021

Instructors: Alberini, Giulia (Fall) Alberini, Giulia (Winter)

• 3 hours

• Prerequisites: Familiarity with a high level programming language and CEGEP level Math.

• Students with limited programming experience should take COMP 202 or equivalent before COMP 250. See COMP 202 Course Description for a list of topics.

• COMP 251 Algorithms and Data Structures (3 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

Computer Science (Sci) : Introduction to algorithm design and analysis. Graph algorithms, greedy algorithms, data structures, dynamic programming, maximum flows.

Terms: Fall 2020, Winter 2021

Instructors: Waldispuhl, Jérôme; Becerra, David (Fall) Becerra, David (Winter)

• 3 hours

• Prerequisite: COMP 250

• Corequisite(s): MATH 235 or MATH 240.

• COMP 251 uses mathematical proof techniques that are taught in the corequisite course(s). If possible, students should take the corequisite course prior to COMP 251.

• COMP 251 uses basic counting techniques (permutations and combinations) that are covered in MATH 240 but not in MATH 235. These techniques will be reviewed for the benefit of MATH 235 students.

• Restrictions: Not open to students who have taken or are taking COMP 252.

• COMP 273 Introduction to Computer Systems (3 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

Computer Science (Sci) : Number representations, combinational and sequential digital circuits, MIPS instructions and architecture datapath and control, caches, virtual memory, interrupts and exceptions, pipelining.

Terms: Fall 2020, Winter 2021

Instructors: Siddiqi, Kaleem (Fall) Lin, Hsiu-Chin; Kry, Paul (Winter)

• COMP 302 Programming Languages and Paradigms (3 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

Computer Science (Sci) : Programming language design issues and programming paradigms. Binding and scoping, parameter passing, lambda abstraction, data abstraction, type checking. Functional and logic programming.

Terms: Fall 2020, Winter 2021

Instructors: Pientka, Brigitte (Fall) Miloslavov, Ivan (Winter)

• COMP 310 Operating Systems (3 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

Computer Science (Sci) : Control and scheduling of large information processing systems. Operating system software - resource allocation, dispatching, processors, access methods, job control languages, main storage management. Batch processing, multiprogramming, multiprocessing, time sharing.

Terms: Fall 2020, Winter 2021

Instructors: Maheswaran, Muthucumaru (Fall) Vybihal, Joseph P; Balmau, Oana (Winter)

• COMP 330 Theory of Computation (3 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

Computer Science (Sci) : Finite automata, regular languages, context-free languages, push-down automata, models of computation, computability theory, undecidability, reduction techniques.

Terms: Fall 2020, Winter 2021

Instructors: Hatami, Hamed (Fall) Panangaden, Prakash (Winter)

• COMP 360 Algorithm Design (3 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

Computer Science (Sci) : Advanced algorithm design and analysis. Linear programming, complexity and NP-completeness, advanced algorithmic techniques.

Terms: Fall 2020, Winter 2021

Instructors: Hatami, Hamed; Kemme, Bettina; Hosseini, Seyyed Aliasghar (Fall) Robere, Robert; Hosseini, Seyyed Aliasghar (Winter)

• MATH 222 Calculus 3 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.

Terms: Fall 2020, Winter 2021, Summer 2021

Instructors: Fortier, Jérôme; Kelome, Djivede (Fall) Vetois, Jerome (Winter)

• MATH 235 Algebra 1 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Sets, functions and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. Rings, ideals and quotient rings. Fields and construction of fields from polynomial rings. Groups, subgroups and cosets; group actions on sets.

Terms: Fall 2020

Instructors: Wise, Daniel (Fall)

• Fall

• 3 hours lecture; 1 hour tutorial

• Prerequisite: MATH 133 or equivalent

• MATH 236 Algebra 2 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Linear equations over a field. Introduction to vector spaces. Linear mappings. Matrix representation of linear mappings. Determinants. Eigenvectors and eigenvalues. Diagonalizable operators. Cayley-Hamilton theorem. Bilinear and quadratic forms. Inner product spaces, orthogonal diagonalization of symmetric matrices. Canonical forms.

Terms: Winter 2021

Instructors: Tserunyan, Anush (Winter)

• MATH 242 Analysis 1 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.

Terms: Fall 2020

Instructors: Hundemer, Axel W (Fall)

• Fall

• Prerequisite: MATH 141

• Restriction(s): Not open to students who are taking or who have taken MATH 254.

• MATH 315 Ordinary Differential Equations (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.

Terms: Fall 2020, Winter 2021, Summer 2021

Instructors: Paquette, Courtney (Fall) Shirazi, Mohammad (Winter)

• Prerequisite: MATH 222.

• Corequisite: MATH 133.

• Restriction: Not open to students who have taken or are taking MATH 325.

• MATH 317 Numerical Analysis (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.

Terms: Fall 2020

Instructors: Bartello, Peter (Fall)

• MATH 318 Mathematical Logic (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Propositional logic: truth-tables, formal proof systems, completeness and compactness theorems, Boolean algebras; first-order logic: formal proofs, Gödel's completeness theorem; axiomatic theories; set theory; Cantor's theorem, axiom of choice and Zorn's lemma, Peano arithmetic; Gödel's incompleteness theorem.

Terms: Fall 2020

Instructors: Tserunyan, Anush (Fall)

• MATH 323 Probability (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.

Terms: Fall 2020, Winter 2021, Summer 2021

Instructors: Sajjad, Alia; Wolfson, David B (Fall) Wolfson, David B; Sajjad, Alia (Winter)

• Prerequisites: MATH 141 or equivalent.

• Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus

• Restriction: Not open to students who have taken or are taking MATH 356

• MATH 340 Discrete Mathematics (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.

Terms: Winter 2021

Instructors: Fortier, Jérôme (Winter)

#### Complementary Courses (18 credits)

9 credits from the set of courses recommended for a major or honours program in Mathematics.

9 credits selected from Computer Science courses at the 300 level or above (except COMP 364 and COMP 396) and ECSE 508.

Faculty of Science—2020-2021 (last updated Mar. 27, 2020) (disclaimer)