An Honours degree offers an in-depth preparation in undergraduate mathematics, including an independent research experience. This degree option is recommended for students interested in eventually pursuing graduate studies in mathematics. Honours students complete a minimum of 54 credit hours above the 1000 level in Mathematics with a minimum GPA of 3.0 and write an Honours Comprehensive Examination.

#### Admission to Honours

Students must apply for admission to Honours programs. Students considering Honours in Mathematics should consult with a Mathematics Honours Advisor early in their studies to have their programs approved.

#### Departmental requirements

The Department offers two Honours streams in Mathematics: (A) Pure Mathematics and (B) Applied Mathematics. Stream A emphasizes the power and beauty of mathematics as an independent academic discipline. Stream B emphasizes the connections between mathematics and other scientific disciplines. Both streams follow the same courses for the first two years. Students decide which stream to pursue during their second year.

In addition to fulfilling the requirements outlined in the Academic Regulations and College of Arts and Science Degree Requirements sections, students in a BSc Concentrated Honours program in Mathematics must complete the following courses:

##### 1000 level

- Math 1030.03: Matrix Theory and Linear Algebra

##### 2000 level

- MATH 2001.03: Intermediate Calculus I/MATH 2002.03: Intermediate Calculus II

Math 2135.03: Linear Algebra and Math 2505.03: Introductory Analysis - Fifteen additional credit hours in mathematics at or above the 2000 level - not including courses listed below

##### 3000 level

- MATH 3031.03: Abstract Algebra I and MATH 3501.03: Intermediate Analysis I
- Students in Stream A are required to take MATH 3032.03: Abstract Algebra II and MATH 3502.03: Intermediate Analysis II
- Students in Stream B are required to take MATH 3080.03: Introduction to Complex Variables and (MATH 3120.03: Differential Equations or MATH 3260.03: Applied Differential Equations)

##### 4000 level

- MATH 4950.03: Honours Research Project
- Twelve additional credit hours at or above the 4000 level

Note: Students will not receive credit for taking MATH 1115.03 after receiving credit for MATH 1000.03, MATH 1500X, or MATH 1215.03

##### Programming requirement

- Students must complete a 3-credit course that incorporates computer programming. Suggested course is one of CSCI 2202, MATH/STAT 2300, PHYC2050/MATH2052, or permission of advisor.

Students in Stream A are advised to include a selection of courses from the following list in their programs:

- MATH 2051.03: Problems in Geometry
- MATH 2113.03: Discrete Structures II
- MATH 3045.03: Curves and Surfaces
- MATH 3070.03: Theory of Numbers
- MATH 3080.03: Introduction to Complex Variables
- MATH 3120.03: Differential Equations
- MATH 3330.03: Applied Graph Theory
- MATH 3360.03: Probability

Students in Stream B are advised to include a selection of courses from the following list in their programs:

- MATH 2060.03: Introduction to Probability and Statistics
- MATH 2300.03: Mathematical Modelling
- MATH 3032.03: Abstract Algebra II
- MATH 3045.03: Curves and Surfaces
- PHYC 3050.03: Introduction to Numerical Programming
- MATH 3300.03: Optimization
- MATH 3330.03: Applied Graph Theory
- MATH 3360.03: Probability
- MATH 3400.03: Classical Game Theory
- MATH 3502.03: Intermediate Analysis II
- MATH 3900.03: Financial Mathematics

#### Honours Comprehensive Examination

The Honours Comprehensive Examination in mathematics consists of a written paper of about 20-30 pages researched and prepared by the student. The topic is decided on in conjunction with the Honours advisor. The paper is also presented to the honours seminar. The work for this paper is done as part of the required course MATH 4950.03: Honours Research Project.