# Mathematics - Bachelor of Science

## Overview

Mathematics is the study of numbers, shapes and relationships through the use of deductive reasoning, and includes both the elegance of pure theory and the application of this theory to all human endeavours. As a mathematics student, you will study topics from the fields of algebra, analysis, geometry and applied mathematics. You'll be rewarded for you hard work with sophisticated analytical tools, a highly developed ability in precise critical thinking, and a general knowledge of the main streams of mathematical thought and their applications to various disciplines.

**Contact Information**

Department of Mathematics and Statistics

Room 5-107, City Centre Campus

10700 - 104 Avenue

Edmonton, AB T5J 4S2

T: 780-497-5786

Faculty of Arts and Science, Program Services (Advising)

Room 6-211, City Centre Campus

T: 780-497-4505

E: artsandscience@macewan.ca

## Bachelor of Science

*Faculty of Arts and Science*

MacEwan.ca/Science

The Bachelor of Science (BSc) is a foundational general degree that provides broad and widely applicable knowledge and abilities, rather than a niche specialization. This broad base equips graduates with generalist knowledge and skills that give the flexibility and agility so highly valued in a dynamic world economy. It also gives students a solid foundation from which to specialize in future employment or further schooling.

The degree provides breadth of study across a variety of Arts and Science disciplines, and sets the foundation for later years. The major and minor areas of study allow students to focus and gain in-depth expertise in complementary or entirely disparate disciplines; there is a wide array of possible combinations. Finally, options allow students to explore courses outside their disciplines, or even within their program, and so enhance their diversity of learning. The small classes, close interaction between instructors and students, opportunities for individual study, and faculty with a strong focus on teaching are signature strengths of this program.

### General Program Information

The BSc requires students to complete 120 credits of non-duplicative coursework. The BSc emphasizes both breadth and depth and has been designed for exceptional flexibility and customization. Students can complete a major and a minor, a double major, or a major and two minors.

### Science Disciplines

Discipline | Major | Minor | Honours |
---|---|---|---|

Applied Statistics | ⦿ | - | - |

Biological Sciences | ⦿ | ⦿ | ⦿ |

Chemistry | ⦿ | ⦿ | - |

Computer Science | ⦿ | ⦿ | - |

Earth and Planetary Sciences | - | ⦿ | - |

Mathematics | ⦿ | ⦿ | ⦿ |

Mathematical Sciences | ⦿ | - | - |

Planetary Physics | - | ⦿ | - |

Physical Sciences | ⦿ | - | - |

Physics | - | ⦿ | - |

Psychology | ⦿ | ⦿ | ⦿ |

Statistics | - | ⦿ | - |

### Arts Minors

Discipline | Minor |
---|---|

Anthropology | ⦿ |

Classics | ⦿ |

Creative Writing | ⦿ |

Economics | ⦿ |

English | ⦿ |

French | ⦿ |

Gender Studies | ⦿ |

History | ⦿ |

Philosophy | ⦿ |

Political Science | ⦿ |

Sociology | ⦿ |

Spanish | ⦿ |

### Out of Faculty Minors

Discipline | Minor |
---|---|

Accounting Minor for Arts and Science | ⦿ |

Arts and Cultural Management | ⦿ |

Business Law | ⦿ |

Business Studies | ⦿ |

Digital Experience Design | ⦿ |

Finance Minor for Arts and Science | ⦿ |

Human Resources Minor for Arts and Science | ⦿ |

Marketing Minor for Arts and Science | ⦿ |

**Preparing for Professional Studies**

Students intending to enter professional programs at other universities can take their pre-professional programs in the Faculty of Arts and Science at MacEwan University. The university offers the first and second year of a number of pre-professional programs, including chiropractic medicine, dental hygiene, dentistry, medical laboratory science, medicine, optometry, pharmacy and veterinary medicine. All courses taken in these pre-professional programs are credit courses and, as such, they may be applied to any of the degrees offered by MacEwan University.

Students are advised to consult the admissions requirements for the universities and programs of their choice, and to select their MacEwan University courses accordingly. Completion of pre-professional courses at MacEwan University does not guarantee admission to the subsequent professional program. Each professional program requires a separate application and entry is competitive, not automatic.

## Degree Requirements

### Breadth Requirements

All Bachelor of Science degrees require Breadth Requirements. Courses can satisfy both the breadth requirements and requirements for the major(s), minor(s), Honours, or options. BIOL, CHEM, EASC, or PHYS courses must include a laboratory component.

Breadth Element | Description | Credits |
---|---|---|

Biological or Earth and Planetary Sciences | BIOL or EASC (not including BIOL 101, BIOL 102, or BIOL 103) | 6 |

Chemistry or Physics | CHEM or PHYS | 6 |

English | ENGL 102 and 3 credits in university English (not including ENGL 111, ENGL 108, or ENGL 211) | 6 |

Humanities | CLAS, COMP, HIST, HUMN, PHIL or a language other than English | 6 |

Mathematical Sciences | One of MATH 114, MATH 120, or MATH 125, and 3 credits in MATH, STAT, or CMPT (not including MATH 160, MATH 170, or CMPT 104) | 6 |

Social Sciences | ANTH, ECON, LING, POLS, PSYC, or SOCI | 6 |

### Bachelor of Science Degree

Program Element | Description | Credits |
---|---|---|

Primary Major | The Science major will range from 42 to 60 credits with a minimum 36 credits taken at the senior-level.^{1} | 42-60 |

Secondary Major or Minor(s) | Students have the option of completing a second Science major, or one or two minors. Minor courses must be completed at the senior-level.^{1} | 18-60 |

Options | Students can complete up to 15 credits in out-of-faculty options, with no more than 3 credits in physical activity (PACT) courses | Up to 60 |

Total Degree Credits Including Breadth | 120 |

^{1} | Multi-disciplinary majors consist of 60-72 junior- and senior-level credits. Students majoring in mathematical or physical sciences may pursue a minor but are not required to do so. |

### Bachelor of Science Honours

Program Element | Description | Credits |
---|---|---|

Minimum Honours Requirements | Honours requirements are determined by each discipline. | 63 |

Option Courses, Non-Compulsory Honours Courses, and/or a Minor | Students have the option of completing a minor from outside of the Honours discipline. Some disciplines may require a minor. | 57 |

Total Degree Credits Including Breadth | 120 |

The minimum passing grade for a course at MacEwan University is a D unless otherwise noted next to the appropriate course in the program of study. In the Faculty of Arts and Science, students typically require a minimum grade of C- to use a course as a prerequisite. Please check course descriptions for more information.

## Mathematics Requirements

### Mathematics Major

The Bachelor of Science (BSc) in Mathematics program requires students to complete 120 credits of non-duplicative coursework. In addition to the Mathematics Major, students will complete one of the following:

- one minor,
- two minors, or
- a secondary Science major

Students are required to complete option courses as well as the major(s) and minor(s). All BSc degrees require Breadth Requirements. Courses can satisfy both the breadth requirements and requirements for the major(s), minor(s), or options.

The Mathematics Major is 45 to 60 credits with a minimum of 36 senior-level credits and a minimum of six credits at the 400-level.

**Note:** Students majoring in Mathematics are required to complete CMPT 101 or CMPT 103.

##### Bachelor of Science - Mathematics Major

Course ID | Course Name | Credits |
---|---|---|

Specific Major Requirements | ||

MATH 114 | Elementary Calculus I | 3 |

MATH 115 | Elementary Calculus II | 3 |

MATH 200 | Fundamental Concepts of Math | 3 |

MATH 214 | Intermediate Calculus I | 3 |

MATH 215 | Intermediate Calculus II | 3 |

MATH 225 | Linear Algebra II | 3 |

MATH 310 | Real Analysis | 3 |

MATH 330 | Ordinary Differential Equations | 3 |

Choose 3 credits from the following: | 3 | |

Basic Linear Algebra I | ||

Linear Algebra I | ||

Choose 3 credits from the following: | 3 | |

Algebra: Introduction to Ring Theory | ||

Geometry | ||

General Major Requirements | ||

Choose 15 to 30 credits from the following: | 15-30 | |

Senior-level MATH | ||

Probability Theory I | ||

Mathematical Statistics | ||

STAT 312 | Probability Theory II | |

Finite Markov Chains and Applications | ||

Secondary Major or Minor(s) | ||

Students have the option of completing a second Science major, or one or two minors. Minor courses must be completed at the senior-level. | 18-60 | |

Options | ||

Students can complete up to 15 credits in out-of-faculty options, with no more than 3 credits in physical activity (PACT) courses. | 0-60 | |

Total Credits | 120 |

### Mathematics Honours

The Bachelor of Science (BSc) Mathematics Honours degree program requires students to complete 120 credits of non-duplicative coursework. The Mathematics Honours program is comprised of 81 to 84 credits with a minimum of 12 credits at the 400-level. Students are required to declare a minor subject as part of the Mathematics Honours requirements. Minors are comprised of 18 senior-level credits.

For admittance/acceptance into Mathematics Honours, students must present the following:

- Completion of a minimum of 45 university-level credits applicable to the program of study, with a GPA of 3.0 or higher
- 24 of the 45 credits must have been completed in the last 12 months
- A minimum of six MATH credits completed at the senior-level
- A minimum GPA of 3.3 across all senior-level MATH courses

Students accepted and enrolled in the Mathematics Honours program must maintain a minimum overall GPA of 3.0. As well, students must maintain a minimum GPA of 3.3 across all senior-level MATH courses and STAT 265, STAT 266, or STAT 322 (if completed) for each 12 consecutive months following acceptance into the Honours program. Failure to maintain a 3.3 Honours GPA will result in the student's program status reverting to a BSc Mathematics Major.

All BSc degrees require Breadth Requirements. Courses can satisfy both the breadth requirements and requirements for Honours, minor(s), or options.

##### Bachelor of Science - Mathematics Honours

Course ID | Course Name | Credits |
---|---|---|

Specific Honours Requirements | ||

MATH 114 | Elementary Calculus I | 3 |

MATH 115 | Elementary Calculus II | 3 |

MATH 200 | Fundamental Concepts of Math | 3 |

MATH 214 | Intermediate Calculus I | 3 |

MATH 215 | Intermediate Calculus II | 3 |

MATH 225 | Linear Algebra II | 3 |

MATH 228 | Algebra: Introduction to Ring Theory | 3 |

MATH 241 | Geometry | 3 |

MATH 310 | Real Analysis | 3 |

MATH 311 | Theory of Functions of a Complex Variable | 3 |

MATH 321 | Fields and Modules | 3 |

MATH 330 | Ordinary Differential Equations | 3 |

MATH 410 | Analysis and Topology | 3 |

MATH 499 | Honours Thesis | 3 |

Choose 3 credits from the following: | 3 | |

Basic Linear Algebra I | ||

Linear Algebra I | ||

General Honours Requirements | ||

Honours Requirements | ||

Choose 18 to 21 credits from the following: | 18-21 | |

Senior-level MATH | ||

Probability Theory I | ||

Mathematical Statistics | ||

STAT 312 | Probability Theory II | |

Finite Markov Chains and Applications | ||

Required Minor | ||

Minor discipline chosen in consultation with the Mathematics Honours advisor | 18 | |

Option Courses | ||

Students can complete up to 15 credits in out-of-faculty options, with no more than 3 credits in physical activity (PACT) courses. | 36-39 | |

Total Credits | 120 |

### Mathematics Minor

The Mathematics Minor requires 18 senior-level MATH credits with a minimum of six credits at the 300- or 400-level.

**Note:** Junior-level required courses MATH 114, MATH 115, and one of MATH 120 or MATH 125.

Course ID | Course Name | Credits |
---|---|---|

Minor Requirements | ||

Choose 18 credits from the following: | 18 | |

Senior-level MATH | ||

Probability Theory I | ||

Mathematical Statistics | ||

STAT 312 | Probability Theory II | |

Finite Markov Chains and Applications | ||

Total Credits | 18 |

## Degree Regulations

Students are strongly encouraged to seek advice from the faculty advisors about program planning.

### Academic Residency - Credit Requirements

In addition to the academic residency requirements of the University, Bachelor of Science students must complete at MacEwan University:

- A minimum of 24 credits at the senior-level in the major discipline, with 12 of those senior credits completed at the 300- or 400-level. All 400-level requirements are to be completed at MacEwan University.
- If applicable, a minimum of nine credits in a minor at the senior-level, with at least three of those credits completed at the 300- or 400-level.

### Breadth Requirements

Courses taken to fulfil the major, minor, or option requirements can also be used to satisfy breadth requirements.

### Declaration of a Major and Minor

Students are advised to declare a primary major and minor, or primary major and a secondary major, or a major and two minors by the time they have completed 45 credits. Majors are selected from Science disciplines and consist of 42 to 60 junior- and senior-level credits. Multi-disciplinary majors consist of 60-72 junior- and senior-level credits. With the exception of those students in an Honours program, a maximum of 60 credits may be completed from any one discipline for credit towards the degree. A major and minor cannot be in the same discipline and students may not declare more than one out-of-faculty minor. Students can re-declare their major(s) and/or minor(s) if required.

For students completing multiple majors or minors, the Faculty cannot guarantee a schedule of classes that will permit students to complete their degree in eight consecutive fall and winter semesters. Furthermore, depending on the courses in which a student enrols, meeting the requirements of a double major may require the completion of more than 120 credits for graduation. Students are strongly encouraged to consult with a program advisor in the Program Services Office in the Faculty of Arts and Science and a discipline advisor in their major and minor prior to this declaration. Students majoring in mathematical or physical sciences may pursue a minor but are not required to do so.

### Graduation Grade Point Average

As part of the Graduation Grade Point Average regulation above, Bachelor of Science students must obtain an overall GGPA of 2.0 or higher, with a minimum GPA of 2.0 on all courses credited toward the major(s) and a minimum GPA of 2.0 on all courses credited toward the minor(s).

### Graduation Requirements

Graduation requirements are governed by the date on which a student declares their major(s) and minor(s). Students who declare their major(s) and minor(s) up to and including February 15 are bound by the requirements of the current academic year. Those students who declare after this date are bound by the programs of study and degree requirements of the upcoming academic year as published in the MacEwan Academic Calendar.

### Junior - and Senior-Level Courses

Courses numbered from 100 to 199 are considered junior-level and courses numbered from 200 to 499 are considered senior-level.

### Major or Minor 300- and 400- Level Requirements

The 300- and 400-level requirements in the major or minor cannot consist solely of project, field placement, and/or individual study courses.

### Maximum Independent Courses

The maximum number of credits for independent work (project, field placement, and/or individual study courses) excluding the Honours Thesis, is 15 credits. Specific disciplines may have further restrictions.

### Maximum Junior-Level Courses

A maximum of 48 credits at the 100-level are permitted in completion of the B.Sc. degree. Additional courses at the 100-level are extra to the 120 credits required to complete the B.Sc. degree and will not be counted toward fulfilment of graduation requirements.

### Minimum Science Courses

Students are required to complete successfully a minimum of 72 total credits from Science courses.

### Minimum Passing Grade

A minimum grade of D is required for all Science degree courses unless otherwise noted next to the appropriate course in the program of study.

### Minimum Transfer Grade for Credit

A minimum grade of D is required on any transfer credit granted for the program. Arts and Science courses require a minimum grade of C- when the course is used as a prerequisite. Transfer credit decisions made by the university are final and cannot be appealed.

### Out-of-Faculty Options Requirements

Degree options may include a maximum of 15 credits from courses offered by a Faculty or School other than Arts and Science except for those students completing an out-of-faculty minor or those who have met the minor requirements with a diploma. These students must complete their degree options from courses offered within the Faculty of Arts and Science.

### Progression of Studies

Students are responsible for ensuring they meet the prerequisite and/or co-requisite requirements as noted on all courses that may fulfill Bachelor of Science program requirements.

## Honours Regulations

### Overall Requirements

The Honours program of study consists of 63 to 84 credits as determined by the discipline. Students in the Honours program may choose to complete a minor outside of the Honours discipline. Some disciplines may require a minor.

### Course Load

Students accepted into an Honours program must complete 24-credits in each twelve consecutive months they are in the program. Exceptions to this rule may occur with the approval of the Honours discipline advisor.

### Grade Point Average

Students accepted and enrolled in the Science Honours program must maintain a minimum overall GPA of 3.0. As well, students must maintain a minimum GPA of 3.3 across a set of courses designated by each discipline for each twelve consecutive months following acceptance into the Honours program. Failure to do so will result in the student’s program status reverting to BSc with a major in the previous Honours discipline.

### Graduation Grade Point Average

In order to graduate, students must obtain an overall GGPA of 3.0 or higher, with a minimum GPA of 3.3 on all courses credited toward the Honours program of study.

## Additional Degree Regulations - Subsequent Baccalaureate

In addition to meeting the degree regulations listed above, students who already hold a baccalaureate degree must satisfy the provisions of policies pertaining to subsequent baccalaureate credentials.

## Mathematics Courses

**MATH 099
Precalculus Mathematics
3 Credits**

This course reviews and extends the mathematical concepts needed to be successful in university level calculus. Topics include graphing, equations of lines, inequalities, review of elementary algebra, functions, and trigonometry. MATH 099 cannot be used to fulfill the requirements of the Bachelor of Arts, the Bachelor of Commerce, or the Bachelor of Science programs.

*Prerequisites: Mathematics 30-1 or Mathematics 30-2.*

**MATH 100
Calculus I
3.5 Credits**

This course provides an introduction to the fundamentals of calculus. The students learn about rectangular coordinates, analytic geometry, transcendental functions, inverse functions, limits, continuity, derivatives and applications, Taylor polynomials, integration and applications. Note: This course is restricted to Engineering students. Credit can only be obtained in one of MATH 100 or MATH 113 or MATH 114.

*Prerequisites: Mathematics 30-1 and Mathematics 31.*

**MATH 101
Calculus II
3.5 Credits**

This course provides a continuation of the study of Calculus. Students learn about techniques of integration, arc length, area of a surface of revolution, applications to physics and engineering, first order ordinary differential equations (separable and linear), infinite series, power series, Taylor expansions, polar coordinates, rectangular coordinates in R3, parametric curves in the plane and space (graphing, arc length, curvature), normal, binormal, tangent in R3. Note: This course is restricted to Engineering Program students. Credit can only be obtained in one of MATH 101 or MATH 115.

*Prerequisites: Minimum grade of C- in MATH 100.*

**MATH 102
Applied Linear Algebra
3.5 Credits**

This course provides an introduction to the fundamentals of linear algebra and some of their applications. The course content includes vectors and matrices; solutions of linear equations; equations of lines and planes; determinants; matrix algebra, linear transformations and their matrices; general vector spaces and inner product spaces; orthogonality and Gram-Schmidt process; eigenvalues and eigenvectors; and complex numbers. Note: This course is restricted to Engineering students. MATH 100 may be taken as a co-requisite with consent of the department. The course may not be taken for credit if credit has already been obtained in MATH 120 or MATH 125.

*Prerequisites: A minimum grade of C- in MATH 100.*

**MATH 114
Elementary Calculus I
3 Credits**

This course examines the fundamental concept of limits, differentiation and integration. Limits and differentiation of algebraic and trigonometric functions are studied along with applications including related rates, optimizing and curve sketching. This course concludes with a study of Riemann sums, the Fundamental Theorem of Calculus and substitution. Note: Students who have received credit in MATH 113 or MATH 100 may not take MATH 114 for credit.

*Prerequisites: A minimum grade of 80% in Mathematics 30-1, or successful completion (50% or better) of Mathematics 31, or Minimum grade of C- in MATH 099, or successful completion of the MATH 114 gateway exam.*

**MATH 115
Elementary Calculus II
3 Credits**

This course investigates the differentiation and integration of trigonometric, exponential and logarithmic functions. Indeterminate forms and improper integrals are studied, as well as the techniques and applications of integration. Note: Credit can only be obtained in one of MATH 115 or MATH 101.

*Prerequisites: Minimum grade of C- in MATH 114.*

**MATH 120
Basic Linear Algebra I
3 Credits**

This is an introduction to the basic notions and methods of linear algebra. Topics covered are: systems of linear equations, vectors in n-space, vector equations of lines and planes, dot product, cross product, and orthogonality, matrix algebra, invertibility of matrices, determinants, general vector spaces, basis and dimension, subspaces of n-space, rank, introduction to linear transformations, introduction to eigenvalues and eigenvectors, and applications. NOTE: This course cannot be taken for credit if credit has already been obtained in either of MATH 102 or MATH 125.

*Prerequisites: Mathematics 30-1 or a minimum grade of 80% in Mathematics 30-2.*

**MATH 125
Linear Algebra I
3 Credits**

This is an enriched introduction to the basic notions and methods of linear algebra. Topics covered are: systems of linear equations, vectors in n-space, vector equations of lines and planes, dot product, cross product, orthogonality, matrix algebra, invertibility of matrices, determinants, general vector spaces, basis and dimension, subspaces of n-space, rank, introduction to linear transformations, introduction to eigenvalues and eigenvectors, and applications. NOTE: The course covers the same basic topics as MATH 120, however it is a more rigorous course, and selected topics and applications are covered in more depth.

*Prerequisites: Mathematics 30-1.*

**MATH 160
Higher Arithmetic
3 Credits**

This course emphasizes the development of clarity in the understanding of mathematical ideas and processes, communication of these ideas to others, and application of these ideas to problem solving. Both inductive and deductive methods are explored in the study of elementary number theory, numeration systems, operations on integers and rational numbers, and elementary probability theory. Note: This course is restricted to Elementary Education students.

*Prerequisites: Mathematics 30-1 or Mathematics 30-2 or successful completion of the gateway exam.*

**MATH 200
Fundamental Concepts of Math
3 Credits**

This course provides an introduction to axiomatic systems and mathematical proof. These ideas are developed using examples taken primarily from set theory and number theory.

**MATH 214
Intermediate Calculus I
3 Credits**

This course completes the study of single-variable calculus and introduces students to the basic concepts of multi-variable calculus. Topics in single-variable calculus include area and arc length of plane curves defined by parametric or polar equations, infinite series, and power series. Topics in multi-variable calculus include: vector functions and space curves, functions of several variables, and partial derivatives with applications.

*Prerequisites: Minimum grade of C- in MATH 115, and in either MATH 120 or MATH 125.*

**MATH 215
Intermediate Calculus II
3 Credits**

This course continues the study of multivariable calculus. Topics include: curves, tangent vectors, arc length; integration in two and three dimensions; polar, cylindrical and spherical coordinates; line and surface integrals, Green’s, divergence and Stokes’ theorems; first and second order linear differential equations.

*Prerequisites: Minimum grade of C- in MATH 214.*

**MATH 222
Discrete Mathematics
3 Credits**

This course is an introduction to discrete mathematics, covering coding, cryptography, induction and recursion, and graph theory. Secret codes, error-detecting and error-correcting codes are introduced. Induction and recursive definitions are described. The Eulerian tour is used to illustrate graph definitions and properties.

*Prerequisites: Minimum grade of C- in any 100-level MATH course.*

**MATH 223
Introduction to Combinatorics
3 Credits**

This course is an introduction to Combinatorics covering permutations, combinations, binomial coefficients, the binomial theorem, the pigeonhole principle, inclusion-exclusion principle, generating functions, recurrences and applications to graph theory.

*Prerequisites: A minimum grade of C- in any 100-level Mathematics course, not including MATH 160 or MATH 170.*

**MATH 225
Linear Algebra II
3 Credits**

This course introduces the theory of vector spaces, inner product spaces, linear transformations and diagonalization. Specific topics of study include Euclidean n-space, spaces of continuous functions, matrix spaces, Gram-Schmidt process, QR-factorization, least squares method, change of basis, eigenspaces, orthogonal diagonalization, quadratic forms, matrices of transformations and similarity. Various applications are presented.

**MATH 228
Algebra: Introduction to Ring Theory
3 Credits**

This course is an introduction to the theory of rings including integral domains, division rings, ring homomorphisms, ideals, quotient rings, fields of quotients, rings of polynomials, irreducible polynomials, Euclidean domains and fields. Specific topics include the well-ordering axiom, the Binomial Theorem, the Euclidean algorithm, the Fundamental Theorem of Arithmetic, and the Chinese Remainder Theorem.

*Prerequisites: A minimum grade of C- in either MATH 200 or MATH 241 and in either MATH 120 or MATH 125.*

**MATH 241
Geometry
3 Credits**

The course explores Euclidean Geometry as an axiomatic system, based on invariance under the group of isometries (rigid motions). The material includes congruence, parallelism, similarity, and the theory of measurements based on continuity axioms. The notion of circumference is introduced and treated rigorously. Problem solving is an important component of the course. The problems include proofs, finding loci, and constructions. Transformations in the Euclidean plane are used as a problem-solving tool.

*Prerequisites: A minimum grade of C- in any 100-level MATH course, not including MATH 160 or MATH 170.*

**MATH 310
Real Analysis
3 Credits**

This course presents a rigorous treatment of limit processes in one variable. Topics include real numbers, sequences, limits, continuous functions, differentiation, the Riemann integral, and the topology of the real number system.

*Prerequisites: Minimum grade of C- in MATH 214 and in MATH 200.*

**MATH 311
Theory of Functions of a Complex Variable
3 Credits**

This course provides an introduction to the fundamental concepts of single variable complex analysis. The main topics include analytic functions, complex power series, Cauchy’s Integral Theorem, Cauchy’s Integral Formula, the residue theorem and applications to improper real integrals and Fourier transforms.

*Prerequisites: Minimum grade of C- in MATH 215.*

**MATH 320
Elementary Number Theory
3 Credits**

Elementary methods in number theory are presented. The following topics are included: divisibility, linear Diophantine equations, prime numbers, the fundamental theorem of arithmetic, congruences, the Chinese remainder theorem, Fermat's little theorem, arithmetic functions, Euler's theorem, primitive roots, and quadratic residues.

*Prerequisites: Minimum grade of C- in MATH 200; A minimum grade of C- in MATH 228 is recommended.*

**MATH 321
Fields and Modules
3 Credits**

This course builds on the knowledge of rings and fields obtained in MATH 228, and introduces the student to basic module theory. Topics studied include finite fields, quadratic number fields and algebraic field extensions, the Fundamental Theorem of Algebra, modules, and Noetherian rings.

*Prerequisites: Minimum grade of C- in MATH 225 and MATH 228.*

**MATH 330
Ordinary Differential Equations
3 Credits**

This course provides techniques for solving ordinary differential equations and systems of first order equations and investigates the qualitative nature of solutions of dynamical systems. Topics covered include first order equations, linear equations of higher order and linear dynamical systems with constant coefficients.

*Prerequisites: Minimum grade of C- in MATH 120 or MATH 125 and in MATH 214.*

**MATH 335
Numerical Methods
3 Credits**

This course presents numerical methods for solving problems in linear algebra, non-linear equations, interpolations, approximation of functions, differentiation and integration. The numerical algorithms are illustrated using an appropriate computer programming language and specific libraries.

*Prerequisites: Minimum grade of C- in MATH 214 and in one of MATH 120 or MATH 125 or CMPT 101.*

**MATH 341
Modern Geometries
3 Credits**

This course explores Euclidean and Non-Euclidean plane geometries from the viewpoint of Klein’s Erlangen program, based on invariance under groups of transformations in the extended complex plane. Mobius geometry is introduced, and Euclidean, hyperbolic, and elliptic geometries are studied as its subgeometries. The differences in axiomatics and results of the Euclidean and Lobachevsky – Bolyai geometries are discussed based on the disc model of hyperbolic geometry. Elliptic geometry is considered as another Mobius subgeometry.

*Prerequisites: Minimum grades of C- in MATH 241, and in either MATH 120 or MATH 125.*

**MATH 350
Introduction to Graph Theory
3 Credits**

This course discusses graphs and digraphs, paths and cycles, trees, planarity, colouring problems and matching problems. In addition, graph algorithms and some applications to other disciplines are studied.

*Prerequisites: Minimum grade of C- in either MATH 120 or MATH 125, and a minimum grade of C- in either MATH 200 or MATH 222.*

**MATH 361
History of Mathematics
3 Credits**

The course is a survey of the history of mathematics from ancient times through the development of calculus and the origins of modern algebra in the nineteenth century. It emphasizes the events that led to the development of modern and classic mathematics from a problem solving perspective. Biographies of famous mathematicians complement the abstract concepts of mathematics.

*Prerequisites: Minimum grade of C- in any two 200-level MATH courses.*

**MATH 398
Independent Study
3 Credits**

This course permits an intermediate-level student to work with an instructor to explore a specific topic from mathematics in depth through research or directed reading in primary and secondary sources. The student plans, executes and reports the results of their independent research or study project under the direction of a faculty supervisor. To be granted enrollment in the course, the student must have made prior arrangements with a faculty member willing to supervise his or her project. This course can be taken twice for credit.

**MATH 410
Analysis and Topology
3 Credits**

This course continues the study of Analysis begun in MATH 310 and examines differentiation and integration in Rn. Specific topics covered will include: implicit and inverse functions theorems, Fubini’s theorem, differential forms, and the generalized Stokes’ theorem.

*Prerequisites: Minimum grade of C- in MATH 225 and MATH 310.*

**MATH 420
Groups and Galois Theory
3 Credits**

This course is a treatment of symmetry, beginning with groups, then developing the ideas of Galois theory, and finishing with the quintic equation. Topics include groups, normal subgroups, quotient groups, Cayley's Theorem, the Class equation, permutations, group actions, the Sylow theorems, splitting fields, Galois extensions, the Main Theorem of Galois theory, Kummer extensions, cubic, quartic and quintic equations.

*Prerequisites: Minimum grade of C- in MATH 321.*

**MATH 430
Applied Dynamical Systems
3 Credits**

This course presents an introduction to dynamical systems related to ordinary differential equations in the continuous case, or to difference equations in the discrete case. Elementary existence and uniqueness theorems and stability are considered for linear and non-linear systems of ordinary differential equations. Periodic solutions, chaotic attractors, an introduction to bifurcation theory, basic notions of discrete dynamical systems, and deterministic chaos are discussed. Applications are chosen from biology, physics and other areas.

*Prerequisites: Minimum grade of C- in MATH 310 and MATH 330.*

**MATH 436
Introduction to Partial Differential Equations
3 Credits**

The goal of this course is to introduce the student to the mathematical modeling of classical physical systems such as vibrating systems, diffusive processes and steady state phenomena. The course starts with a rigorous introduction of the first-order and linear second-order partial differential equations (PDEs) followed by elements of Fourier analysis. The method of characteristics is used to find and interpret classes of solutions for the above models. The lab component will familiarize the student with formal and numerical manipulations of PDE’s. The main scope of the lab is to enable the student to visualize and discuss solutions for classical models for PDE’s.

*Prerequisites: Minimum grade of C- in MATH 310 and MATH 330.*

**MATH 495
Special Topics in Mathematics
3 Credits**

In this course students examine an advanced topic of specialization in mathematics. Topics covered vary from year to year. Consult with faculty members in Mathematics for details regarding current offerings. Note: This course may be taken multiple times for credit.

*Prerequisites: Minimum grade of B- in a 300-level Math course and permission of the department.*

**MATH 498
Advanced Independent Study in Mathematics
3 Credits**

This course permits a senior-level student to work with an instructor to explore a specific topic from mathematics in depth through research or directed reading in primary and secondary sources. The student plans, executes and reports the results of their independent research or study project under the direction of a faculty supervisor. To be granted enrollment in the course, the student must have made prior arrangements with a faculty member willing to supervise his or her project. This course can be taken twice for credit.

**MATH 499
Honours Thesis
3 Credits**

Under the direction of a faculty supervisor, registered students explore a specific topic in depth through research or directed reading. The student plans, executes, and reports the results of their independent research or study project under the direction of a faculty supervisor in a written Honours Thesis with oral defense. Note: This course is intended for students in the final year of their degree and is open only to students in the Mathematics Honours program.

*Prerequisites: Consent of the Department.*