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4.9.3 Mathematics Course Descriptions-2000 Level
Course Code
 MATH 2020 Credits 3
Title Algebra 1
Description (Lab required) The course is intended for students in mathematically rich disciplines. Groups, rings, fields: elementary concepts and examples. May not be held with MATH 2021 or the former MATH 3350. Prerequisite: MATH 2090 or MATH 2091 (C) or the former MATH 2352 (C) or the former MATH 2300 (B) or MATH 2301 (B).

Course Code
 MATH 2030 Credits 3
Title Combinatorics 1
Description (Lab required) Introductory combinatorics, including basic counting, permutations and combinations, enumeration, inclusion-exclusion, pigeonhole principle, solving basic recursions, relations, and derangements. May not be held MATH 2031 or the former MATH 3400. Prerequisites: MATH 1240 (C) or MATH 1241 (C) or [the former MATH 2202 (C) and one of the former MATH 2350 or the former MATH 2352 (C)] or consent of instructor.

Course Code
 MATH 2040 Credits 3
Title Curves and Surfaces
Description (Lab required) Curves and surfaces in the plane and space. Intrinsic geometry of curves and surfaces: Serret Frenet frames, first and second fundamental forms, curvature and the Gauss map. Geodesics and parallel transport. Theorema Egregium and Gauss-Bonnet theorems. Prerequisites: [MATH 1232 (C) or MATH 1690 (C) or MATH 1700 (B) or MATH 1701 (B) or MATH 1710 (B)] and [MATH 1220 (C) or MATH 1300 (B) or MATH 1301 (B)]; or consent of instructor. Pre-or corequisite: MATH 2150 or MATH 2151 or MATH 2720 or MATH 2721.

Course Code
 MATH 2070 Credits 3
Title Graph Theory 1
Description (Lab required) Introduction to graphs, digraphs, and multigraphs. Topics include trees, cycles and circuits, planarity, basic graph algorithms, and applications of graph theory to social and physical sciences. May not be held with MATH 2071 or the former MATH 2400 or COMP 4340. Prerequisites: [MATH 1240 (C) or MATH 1241 (C)] and [MATH 1220 (C) or MATH 1300 (B) or MATH 1301 (B)].

Course Code
 MATH 2080 Credits 3
Title Introduction to Analysis
Description (Lab required) The course is intended for students in mathematically rich disciplines. Fundamental properties of the real number system as a complete ordered field, Archimedean property, existence of square roots, density of rational numbers, uncountability of real numbers. Sequences, subsequences, limit theorems, monotonicity, Bolzano-Weierstrass theorem, Cauchy sequences. Rigorous treatment of limits and continuity of functions of one and several variables. Uniform continuity. Applications. May not be held with MATH 2081 or the former MATH 2202. Prerequisites: [MATH 1232 (C) or MATH 1690 (C) or MATH 1700 (B) or MATH 1701 (B) or MATH 1710 (B)] and [MATH 1220 (C) or MATH 1300 (B) or MATH 1301 (B)] and [MATH 1240 (C) or MATH 1241 (C)].

Course Code
 MATH 2090 Credits 3
Title Linear Algebra 2
Description (Lab required) The course is intended for students in mathematically rich disciplines. Abstract vector spaces, linear transformations, bases and coordinatization, matrix representations, orthogonalization, diagonalization, principal axis theorem. May not be held with MATH 2091 or the former MATH 2300 or the former MATH 2301 or the former MATH 2350 or the former MATH 2352. Prerequisite: MATH 1220 (C) or MATH 1300 (B) or MATH 1301 (B).

Course Code
 MATH 2120 Credits 4
Title Introductory Numerical Methods for Engineers
Description (Lab Required) Numerical methods applied to problems in engineering; roots of nonlinear equations and systems of linear equations, numerical differentiation and integration, initial-value problems. For Engineering and Geophysics students only. May not be held with MATH 2600 or MATH 2601. Prerequisites: one of COMP 1010, COMP 1011, COMP 1012, COMP 1013 (C); pre- or corequisite: MATH 2132 or the former MATH 2100 (C).

Course Code
 MATH 2130 Credits 3
Title Engineering Mathematical Analysis 1
Description (Lab required) Multivariable differential and integral calculus up to and including multiple integrals in cylindrical and spherical coordinates. For Engineering and Geophysics students only. May not be held for credit with MATH 2720, MATH 2750, or the former MATH 2110. Prerequisites: MATH 1210 or MATH 1211 and MATH 1710 (C).

Course Code
 MATH 2132 Credits 3
Title Engineering Mathematical Analysis 2
Description (Lab required) Infinite series, Taylor and Maclaurin Series; ordinary differential equations including Laplace transforms. For Engineering and Geophysics students only. May not be held for credit with MATH 2800, MATH 2730, or the former MATH 2100. Prerequisites: MATH 1210 (C) or MATH 1211 (C), and MATH 1710 (C).

Course Code
 MATH 2140 Credits 3
Title Modelling
Description (Lab required) Introductory course on the design and analysis of mathematical models for real-life phenomena arising in the natural, engineering and social sciences. May not be held with the former MATH 3820 or the former MATH 3821. Prerequisite: MATH 1230 (C+) or MATH 1690 (C+) or MATH 1500 (B) or MATH 1501 (B) or MATH 1510 (B) or MATH 1220 (C) or MATH 1300 (B) or MATH 1301 (B) or consent of instructor.

Course Code
 MATH 2150 Credits 3
Title Multivariable Calculus
Description (Lab required) The course is intended for students in mathematically rich disciplines. Parametric curves, arc length and curvature. Functions of several variables. Level curves. Partial derivatives, gradient, divergence and curl. Max/min problems. Double and triple integrals, line and surface integrals of functions and vector fields, and applications. Green's, Stokes, and divergence theorems. May not be held with MATH 2130, MATH 2151, MATH 2720, MATH 2721, or the former MATH 2750. Prerequisite: MATH 2080 (C) or MATH 2081 (C) or the former MATH 2202 (C).

Course Code
 MATH 2160 Credits 3
Title Numerical Analysis 1
Description (Lab required) Elementary techniques of numerical solution of mathematical problems: solution of equations, linear systems of equations, nonlinear equations; finite and divided differences, interpolation; numerical differentiation and integration. May not be held with MATH 2120, MATH 2161, the former MATH 2600, or the former MATH 2601. Prerequisites: [MATH 1232 (C) or MATH 1690 (C) or MATH 1700 (B) or MATH 1701 (B) or MATH 1710 (B)] and [MATH 1220 (C) or MATH 1300 (B) or MATH 1301 (B)].

Course Code
 MATH 2170 Credits 3
Title Number Theory 1
Description (Lab required) Prime numbers, unique factorization, linear congruences, Chinese remainder theorem, multiplicative functions, primitive roots and quadratic reciprocity. May not be held with the former MATH 2500 or the former MATH 2501. Prerequisite: (a C" or better in MATH 2090 or MATH 2091) or (a "C" or better in MATH 1240 or MATH 1241) or (a "C" or better in the former MATH 2350 or the former MATH 2352) or (a "B" or better in the former MATH 2300 or the former MATH 2301).

Course Code
 MATH 2180 Credits 3
Title Real Analysis 1
Description (Lab required) Introduction to metric spaces including connectedness, compactness and continuity; topics in infinite series of numbers, and sequences and series of functions. May not be held with the former MATH 3230. Prerequisite: MATH 2080 (C) or MATH 2081 (C) or the former MATH 2202 (C).

Course Code
 MATH 2720 Credits 3
Title Multivariable Calculus
Description Calculus of several variables. For students in one of the following programs: Actuarial Mathematics, Data Science, Statistics (Honours or Majors), Physics (Honours or Majors) Geophysics (Honours or Majors), and Physical Geography. May not be held with the former MATH 2750, the former MATH 2110, MATH 2130, MATH 2150, MATH 2151 or MATH 2721. Prerequisites: (one of MATH 1220, MATH 1300, MATH 1301, or MATH 1310) and (one of MATH 1232, MATH 1690, MATH 1700, MATH 1701, MATH 1710, or the former MATH 1730).

Course Code
 MATH 2740 Credits 3
Title Mathematics of Data Science
Description (Lab required) This course introduces some of the mathematical tools used in Data Science. Topics include linear algebra: least squares, singular value decomposition, principal components analysis, and graph theory: centrality, social network theory, clustering. This course can only be used as an elective in an Honours, Major, or Joint Honours program in Mathematics. Prerequisites: [(a "B" or better in MATH 1210 or MATH 1211) or (a "C" or better in one of MATH 1220, MATH 1300, or MATH 1301)] and (a "C" or better in one of MATH 1232, MATH 1690, MATH 1700, MATH 1701, or MATH 1710).