# Mathematics Courses

### 100 Level

101 Mathematical Concepts I: Sets, Logic, and Number Theory
This course surveys topics from diverse areas of mathematics, including problem
solving, set theory, logic, historical numeration systems, and number theory.
Students will solve problems using processes such as abstraction, pattern
recognition, deduction and generalization. Credit will be granted for only one of
MATH 101 or MATH 100. Acceptable for credit only in the Faculties of Arts and
Business and the Departments of Human Kinetics, Human Nutrition and Nursing.
Prerequisite: Grade 12 math or equivalent. Three credits.

102 Mathematical Concepts II: Graphs, Functions, Geometry, and Probability
The course surveys interesting and useful topics from diverse areas of mathematics,
including problem solving, algebra, graphs and functions, geometry, counting
methods, and probability. Students will solve problems using processes such
as abstraction, pattern recognition, deduction and generalization. Credit will be
granted for only one of MATH 102 or MATH 100. Acceptable for credit only in the
Faculties of Arts and Business and the Departments of Human Kinetics, Human
Nutrition and Nursing. Prerequisite: Grade 12 math or equivalent. Three credits.

This course will give an introduction to some of the quantitative methods used
in the fields of business. A presentation of mathematics applicable to business,
including functions, modelling, finance, regression, forecasting, simulation, and
linear programming. Use of spreadsheets will be a fundamental part of this course.
Acceptable for credit in all programs. May only be used as an open or an approved
elective in mathematics or computer science programs. Credit will be granted for
only one of MATH 105 and MATH 205. Three credits and one-hour lab.

106 Calculus I
An introduction to differential calculus of a single variable, with applications to
physical, life, and social sciences. Topics include limits, differentiation of polynomial,
exponential, logarithmic, and trigonometric functions, inverse functions and their
derivatives, implicit differentiation, curve sketching, and applied max-min problems.
The format of MATH 106 has been structured to provide students with additional
learning resources to support and foster a conducive learning environment. Credit
will be granted for only one of MATH 106, ENGR 121 or MATH 126. Prerequisite:
Grade 12 pre-calculus or equivalent. Three credits and one-hour problem-session
and one-hour lab.

107 Calculus II
An introduction to integral calculus for functions of one variable. Topics include
definite and indefinite integrals; the fundamental theorem of calculus; methods
of integration; numerical approximation of definite integrals; applications to area
and volume; probability density functions and distributions; differential equations;
and Taylor polynomials. The format of MATH 107 has been structured to provide
students with additional learning resources to support and foster a conducive
learning environment. Credit will be granted for only one of MATH 107, ENGR 122
or MATH 127. Prerequisite: MATH 106 or 111 or 126.Three credits and one-hour
problem-session and one-hour lab.

121 Calculus I for Engineers
This course examines the main idea of calculus of a single variable. It covers
functions, limits, continuity; differentiation and integration of polynomial, exponential,
logarithmic, and trigonometric functions; product, quotient, and chain rules;
applications of differentiation to graphing; maximum-minimum problems, and related
rate problems; definite and indefinite integrals, and the fundamental theorem of
calculus. Credit will be granted for only one of MATH 121 or MATH 106 or 126(111).
Cross-listed as ENGR 121. Prerequisite: grade 12 pre-calculus or equivalent. Three
credits and one-hour lab and one-hour problem session.

122 Calculus II for Engineers
A continuation of ENGR 121, this course covers the applications of integration,
including areas, volumes, moments, pressure, and work; techniques of integration;
numerical integration; length of curves; surfaces of revolution; parametric equations;
polar co-ordinates; sequences and series; and Taylor series. Credit will be granted
for only one of MATH 122 or MATH 107 or 127(112). Cross-listed as ENGR 122.
Prerequisite: MATH 121. Three credits and one-hour lab and one-hour problem
session.

126 Calculus I
An introduction to differential calculus of a single variable, with applications to
physical, life, and social sciences. Topics include limits, differentiation of polynomial,
exponential, logarithmic, and trigonometric functions, inverse functions and their
derivatives, implicit differentiation, curve sketching, and applied max-min problems.
Credit will be granted for only one of MATH 106, ENGR 121 or MATH 126.
Prerequisite: Grade 12 pre-calculus or equivalent. Three credits and a one-hour
lab every other week.

127 Calculus II
An introduction to integral calculus for functions of one variable. Topics include
definite and indefinite integrals; fundamental theorem of calculus; methods of
integration; numerical approximation of definite integrals; applications to area and
volume; probability density functions and distributions; differential equations; and
Taylor polynomials. Credit will be granted for only one of MATH 107, MATH 127
or ENGR 122. Prerequisite: MATH 106 or MATH 111 or MATH 126. Three credits
and a one-hour lab every other week.

### 200 level

221 Differential Equations for Engineers
Covers first order linear and non-linear ordinary differential equations; ordinary
differential equations of higher order with constant coefficients; applications
to engineering problems; power series solutions; Laplace transforms; periodic
functions; applications of Laplace transforms to linear systems; Fourier series.
Credit will be granted for only one of MATH 221 or MATH 367. Cross-listed as
ENGR 221. Prerequisite: MATH 122. Three credits and two-hour problem session.

222 Calculus III for Engineers
Extends the ideas introduced in MATH 121 to the calculus of several variables, and
covers space curves, arclength, curvature; partial derivatives; implicit functions;
constrained and unconstrained extrema; multiple integrals; line, surface, and
volume integrals; change of variables in multiple integrals; scalar and vectors fields;
gradient, divergence, and curl; Stokes theorem. Credit will be granted for only one
of MATH 222 or MATH 267. Cross-listed as ENGR 222. Prerequisite: MATH 122.
Three credits and two-hour problem session.

223 Linear Algebra for Engineers
Covers geometric vectors in three dimensions; dot product; cross product; lines
and planes; complex numbers; systems of linear equations; matrix algebra;
matrix inverse; determinants; Cramer’s rule; introduction to vector spaces;
linear independence and bases; rank; linear transformations; orthogonality and
applications; Gram-Schmidt algorithm; eigenvalues and eigenvectors. Credit will
be granted for only one of MATH 223 or MATH 253. Cross-listed as ENGR 123.
Prerequisites: MATH 122. Three credits and two-hour problem session.

236 Data Modeling for Business
Evidence-based decision-making in business required the use of the mathematical
models to analyze data and to help identify and assess possible answers to what-if
questions. This course introduces the student to what should be considered when
using mathematical models for business. Topics include model construction,
analyzing and modeling data sets, optimization, risk analysis and model testing.
Prerequisite: MATH 106 or 126(111) or 105. Three credits.

253 Matrix Algebra
An introduction to solution of linear systems, algebra of matrices, determinants,
two- and three-dimensional vector spaces, and the matrix eigenvalue problem.
Credit will be granted for only one of MATH 253 or MATH 223. Prerequisite: MATH
101/102 or 107 or 127(112) or 122 or CSCI 162. Three credits.

254 Linear Algebra
An introduction to abstract vector spaces, including discussion of bases, dimension
and homomorphisms of vector spaces; linear transformations, including invariant
subspaces; matrix representations and diagonalization procedures. Prerequisite:
MATH 253. Three credits.

267 Calculus III
Topics include the Taylor polynomial theorem; indeterminate forms and l’Hôpital’s
rule; improper integrals; infinite and power series and tests of convergence;
parametric equations; partial differentiation; and selected concepts from multivariate
differential calculus, and multiple integration. Credit will be granted for only one of
MATH 267 or MATH 222. Prerequisite: MATH 107 or 127(112) or 122. Three credits.

277 Discrete Structures
An introduction to sets, binary relations and operations; induction and recursion;
partially ordered sets; simple combinations; truth tables; Boolean algebras and
elementary group theory, with applications to logic networks, trees and languages;
binary coding theory and finite-state machines. Cross-listed as CSCI 277.
Prerequisite: MATH 101/102 or 107 or 127(112) or 122 or CSCI 162. Three credits.

287 Natural Resource Modelling
The course covers formulating real-world problems from renewable natural
resources; using software to solve mathematical models; formulating and testing
policies for managing dynamic systems; and developing communication skills
through report writing. Prerequisite: MATH 107 or 127(112). Three credits. Offered
2017-2018 and in alternate years.

### 300 Level

335 Management Science
This course prepares students for careers as analysts and consultants in industries
with a focus on enhancing business value through operations, logistics and supply
chain management. A variety of successful implementations of management
science/operations research tools in different application areas will be studied. Tools
such as linear programming, project scheduling with uncertain activity times, various
inventory models and simulation will be introduced and coupled with application in
the fields of managing operations in manufacturing, long term financial planning
and management of healthcare systems. Cross-listed as CSCI 335. Prerequisites:
MATH 106/126 or MATH 105 or CSCI 161. Three credits.

347 Combinatorics
The course covers the principle of inclusion and exclusion; generating functions;
recurrence relations; rings and modular arithmetic; finite state machines; group
and coding theory; Pólya’s method of enumeration; finite field and combinatorial
design; graph theory. Prerequisite: MATH 277. Three credits. Not offered 2017-
2018; next offered 2018-2019.

354 Modern Algebra I
This course introduces algebraic structures such as groups, rings and fields
along with fundamental algebraic concepts such as symmetries, permutations,
isomorphisms and homomorphisms. Applications from diverse areas may
include coding theory, crystallography, circuits, logic, geometry and graph theory.
Prerequisites: MATH 254, 277. Three credits.

361 Advanced Vector Calculus
Topics include vectors; vector differentiation including gradient, divergence, and
curl; vector integration including the Gauss and Stokes theorems. Prerequisites:
MATH 222 or 267 and 223 or 253. Three credits.

366 Real Analysis I
This course considers rigorous development of the real number system; numerical
sequences and series; properties of continuous functions; metric spaces; sequences
and series of functions. Prerequisites: MATH 254, 267 and 277. Three credits.

367 Differential Equations
Topics include first- and second-order linear differential equations; systems of linear
differential equations; methods of solution including Laplace transforms and series
solution; introduction to non-linear differential equations and numerical methods.
Credit will be granted for only one of MATH 367 or MATH 221. Prerequisites: MATH
107 or 127(112). Three credits.

371 Modern Geometries
A brief survey of geometries including projective, affine, similarity, equiareal,
Euclidean, and non-Euclidean. Emphasis is on the invariants of transformational
geometry. Prerequisite: MATH 277. Three credits. Not offered 2017-2018; next
offered 2018-2019.

372 Number Theory
Topics include divisibility of integers; congruences; the Chinese remainder theorem;
quadratic residues and non-residues; Gaussian reciprocity law; number theoretic
functions; and the Moebius inversion formula. Prerequisite: MATH 277. Three
credits. Offered 2017-2018 and in alternate years.

384 Numerical Methods
This course covers methods used to solve mathematical problems on computer
systems, including mathematical background and error analysis of solutions to
non-linear equations; polynomial interpolations; integration and differentiation;
quadrature methods; systems of equations and differential equations. Prerequisites:
MATH 223 or 253; CSCI 161 or 125. Three credits. Offered 2017-2018 and in
alternate years.

387 Mathematical Modelling
This course teaches the use of mathematical models to solve real-world problems.
The modelling cycle will be practiced using problems found in the real world.
Prerequisites: MATH 222 or 267, and MATH 223 or 253. Three credits. Not offered
2017-2018; next offered 2018-2019.

389 Financial Mathematics
Topics include stochastic models of financial markets; forward and futures contracts;
European options and equivalent Martingale measures; hedging strategies and
management of risk; term structure models and interest rate derivatives; and optimal
stopping and American options. Ito’s lemma and Girsanov’s theorem to develop
methods for pricing financial derivatives are examined. Pricing problems are considered
in discrete (Binormal option price model) and continuous-time (Black-Scholes Merton
price model). Credit will be granted for only one of MATH 389 or MATH 471 offered
in 2012-2013. Prerequisites: MATH 106 or 126(111); STAT 101(201) or 231. Three
credits. Offered 2017-2018 and in alternate years.

### 400 Level

454 Modern Algebra II
The topics are: polynomial rings, unique factorization, irreducible polynomials;
Sylow theorems, solvability of polynomial equations; Galois theory; and the Jordan
canonical form. Prerequisite: MATH 354. Three credits. Not offered 2017-2018;
next offered 2018-2019.

462 Complex Variables
Topics include complex numbers, elementary functions, series and integration,
Laurent series, and residue theory. Prerequisites: MATH 221 or 367 and 222 or
361. Three credits. Not offered 2017-2018; next offered 2018-2019.

466 Real Analysis II
Material includes: topology of Euclidean nspace; differentiation; Riemann Stieltjes
integration; limits and continuity in n-dimensions; differentiation of nonlinear
transformations; and the implicit function theorem. Prerequisite: MATH 366. Three
credits. Offered 2017-2018 and in alternate years.

471 Topics in Mathematics
This course will cover current mathematical topics such as graph theory, multivalued
logic, dynamical systems, optimization theory, point set topology or mathematical
finance. Three credits. See http://sites.stfx.ca/mscs/math_courses for more
information.

481 Partial Differential Equations
The study of special functions and partial differential equations, including the wave,
heat, and Laplace equations in various coordinate systems. Prerequisites: MATH
254 and 221 or 367 and MATH 267 or 222. Three credits. Offered 2017-2018 and
in alternate years.

491 Senior Seminar
Cross-listed as CSCI 491 and MATH 491.The purpose of this non-credit course
is to assist students in carrying out research, composition, and oral presentation.
Students will present a project topic in the fall term and their project in the spring.
Attendance at departmental seminars is mandatory. No credit.

493 Senior Thesis
Students will prepare and present a thesis based on original research conducted
under the supervision of a faculty member. Required for honours students; permitted
for advanced major students. Three credits.