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BSc (120 credit hour) Concentrated Honours in Mathematics

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 Ìý²¹²Ô»å sections, students in a BSc Concentrated Honours program in Mathematics must complete the following courses:

1000 level

• .03/.03 (or equivalent)
• .03: Matrix Theory and Linear Algebra I

2000 level

• .03: Intermediate Calculus I/.03: Intermediate Calculus II
  .03: Linear Algebra and .03: Introductory Analysis
• Fifteen additional credit hours in mathematics at or above the 2000 level - not including courses listed below

3000 level

• .03: Abstract Algebra IÌý²¹²Ô»å .03: Intermediate Analysis I
• Students in Stream A are required to take .03: Abstract Algebra IIÌý²¹²Ô»å .03: Intermediate Analysis II
• Students in Stream B are required to take .03: Introduction to Complex VariablesÌý²¹²Ô»å (.03: Differential Equations or MATH 3260.03: Applied Differential Equations)

4000 level

• .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 .03, MATH 1500X, or .03

Programming requirement

• Students must complete a 3-credit course that incorporates computer programming.Ìý Suggested course is one of .03, .03/.03, .03/.03, or permission of advisor.

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

• .03: Problems in Geometry
• .03: Discrete Structures
• .03: Curves and Surfaces
• .03: Theory of Numbers
• .03: Introduction to Complex Variables
• .03: Differential Equations
• .03: Applied Graph Theory
• .03: Probability

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

• .03: Introduction to Probability and Statistics
• .03: Mathematical Modelling
• .03: Abstract Algebra II
• .03: Curves and Surfaces
• PHYC 3050.03: Introduction to Numerical Programming
• .03: Optimization
• .03: Applied Graph Theory
• .03: Probability
• MATH 3400.03: Classical Game Theory
• .03: Intermediate Analysis II
• .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 .03: Honours Research Project.

BSc (120 credit hour) Combined Honours in Mathematics and another subject

Students who wish to study Mathematics in conjunction with another subject may wish to pursue a Combined Honours degree program. The other subject may be any discipline from the Faculty of Science, the Faculty of Arts and Social Sciences, the Faculty of Computer Science, or the College of Sustainability. Mathematics may be the primary subject (defined as the subject with the larger number of honours credits), or the secondary subject. Students contemplating a Combined Honours program in Mathematics and another subject should bear in mind, however, that the work in either subject may be insufficient for admission to a regular graduate program.

Students planning to enrol in a Combined Honours program should consult with academic advisors from both programs early in their studies. The same standards and conditions for admission apply as for entry into a Concentrated Honours program (see above). In addition, students must have their program of study approved by Academic Advisors in both subject areas. Students must complete an Honours Qualifying Examination in one of the two subject areas, a requirement normally completed in the primary subject area. For Mathematics, this requirement is satisfied through .03.

Departmental Requirements

Students in a BSc Combined Honours program in Mathematics and another subject must fulfill the requirements outlined in the Academic Regulations and College of Arts and Science Degree Requirements sections.Ìý A combined total of 66 credit hours above the 1000 level must be completed in two subjects, with a minimum of 30 credit hours above the 1000 level in each subject. In addition, students must complete a minimum of 18 credit hours at the 3000 level or above in each of the primary and secondary subjects.

Students in a BSc Combined Honours program in Mathematics, with Mathematics either as the primary subject or as the secondary subject, must complete the following courses. The program must be approved by a Mathematics Honours Advisor and an Honours advisor from the other subject.

2000 level

•ÌýÌýÌý .03: Intermediate Calculus I
•ÌýÌýÌý .03: Intermediate Calculus II
•ÌýÌýÌý .03: Linear Algebra
•ÌýÌýÌý .03: Introductory Analysis

3000 level

•ÌýÌýÌý At least two of .03: Abstract Algebra I, .03: Abstract Algebra II, .03: Introduction to Complex Variables, (.03: Differential Equations or MATH 3260.03: Applied Differential Equations), .03: Intermediate Analysis I, .03: Intermediate Analysis II

4000 level

•ÌýÌýÌý Six additional credit hours in MATH at the 4000 level

If Mathematics is the primary subject, students must also complete:

•ÌýÌýÌý .03: Honours Research Project

Note: Students will not receive credit for taking MATH 1115.03 after receiving credit for .03, MATH 1500X, or .03

BSc (120 credit hour) Major in Mathematics

The 120 credit hour Major is suited to students who want to focus on Mathematics, but wish to have a program that is somewhat less constrained than the Honours program. Students in a Major program normally choose to concentrate in Pure Mathematics, Applied Mathematics or Mathematics Education.

Departmental Requirements

In addition to fulfilling the requirements outlined in the Ìý²¹²Ô»å Ìýsections, students in a BSc Major program in Mathematics must complete the following courses:

1000 level

• .03/.03 (or equivalent)
• .03: Matrix Theory and Linear Algebra I

2000 level

• .03: Intermediate Calculus I/.03: Intermediate Calculus II
• .03: Matrix Theory and Linear Algebra IIÌý(or .03: Linear Algebra)
• At least one of .03: Logic and set theory (or MATH 2112.03 : Discrete Structures I), .03: Problems in GeometryÌýor .03: Introductory Analysis
• Six additionalÌýcredit hoursÌýin MATHÌýat or above 2000 level
• Three credit hours in aÌýSTAT course at or above 2000 level

3000 level

• 24 additional credit hours in MATHÌýat or above the 3000 level. This selection may not include .03: Mathematics for Economists, .03: Financial Economics.

Programming requirement

• Students must complete a 3-credit course that incorporates computer programming.Ìý Suggested course is one of , /, /, or permission of advisor.

Students wishing to concentrate in Applied Mathematics should choose theÌýadditional MATH courses from

• .03: Introduction to Probability and Statistics/.03: Statistical Methods for Data Analysis and Inference
• .03: Methods for Ordinary Differential Equations/.03: Differential Equations
• .03: Mathematical Modelling
• .03: Differential Equations
• .03: Introduction to Numerical Analysis
• .03: Optimization
• .03: Applied Graph Theory
• MATH 3400.03: Classical Game Theory

Students wishing to concentrate in Pure Mathematics should choose the additional MATH courses from

• .03: Introduction to Probability and Statistics/.03
• .03: Methods for Ordinary Differential Equations/.03: Differential Equations
• .03: Abstract Algebra I/.03: Abstract Algebra II
• .03: Curves and Surfaces
• .03: Theory of Numbers
• .03: Introduction to Complex Variables

Students contemplating a career in Mathematics Education should choose the additional MATH courses from

• .03: Problems in Geometry
• .03: Introduction to Probability and Statistics/.03
• .03: Logic and set theory
• .03: Discrete Structures
• .03: Mathematical Modelling
• .03: Abstract Algebra I/.03: Abstract Algebra II
• .03: Theory of Numbers
• .03: Introduction to Complex Variables
• .03: Introduction to Wavelets
• .03: Optimization
• .03: Applied Graph Theory
• MATH 3400.03: Classical Game Theory

Note: Students will not receive credit for taking MATH 1115.03 after receiving credit for .03, MATH 1500X, or .03

BSc or BA (120 credit hour) Double Major in Mathematics and another subject

The Double Major degree program allows students to combine the study of Mathematics with another subject. The other subject may be any discipline from the Faculty of Science, the Faculty of Arts and Social Sciences, the Faculty of Computer Science or the College of Sustainability. Mathematics may be the primary subject (defined as the subject with the larger number of credits), or the secondary subject. If the primary subject area is from the Faculty of Arts and Social Sciences, the degree granted will be a BA.

Students enrolled in a Double Major program are advised to review their proposed program of study with advisors in both subject areas.

Departmental requirements

In addition to fulfilling the requirements outlined in the Ìý²¹²Ô»å Ìýsections, students in a BSc or BA Double Major program in Mathematics and another subject must complete the following:

Mathematics as the primary subject

Student completing a double major with Mathematics as the primary subject can fulfill the Mathematics requirements by following one of two programs below.

Pure Mathematics

1000 level

• .03/.03 (or equivalent)

2000 level

• .03: Intermediate Calculus IÌý²¹²Ô»å .03: Intermediate Calculus II
• .03: MatrixÌýTheory and Linear Algebra IIÌý(or MATHÌý2135.03: Linear Algebra)
• At least two of .03: Logic and set theory (or MATH 2112.03: Discrete Structures I), .03: Problems in Geometry, .03: Introductory Analysis

3000 level

• 18 additional MATH credit hours at or above the 3000 level. This selection may not include .03: Mathematics for Economists, .03: Financial Economics.

Programming requirement

• Students must complete a 3-credit course that incorporates computer programming.Ìý Suggested course is one of .03, .03/.03, .03/.03, or permission of advisor.

Applied Mathematics

1000 level

• .03/.03 (or equivalent)

2000 level

• .03: Intermediate Calculus I
• .03: Matrix Theory and Linear Algebra IIÌý(or .03: Linear Algebra)
• .03: Methods for Ordinary Differential Equations and .03: Intermediate Calculus II
• .03: Introduction to Probability and StatisticsÌýor .03: Statistical Methods for Data Analysis and Inference

3000 and 4000 levelÌý

• .03 or MATH 3260.03
• At least 15 credit hours selected from : .03, .03, .03, .03, .03, .03, .03, MATH 3400.03, .03, MATH 4190.03, .03, .03, .03, MATH 4320.03, .03, .03.

Programming requirement

• Students must complete a 3-credit course that incorporates computer programming.Ìý Suggested course is one of .03, .03/.03, .03/.03, or permission of advisor.

Mathematics as the secondary subject

A student enrolled in a Double Major with Mathematics as the secondary subject also fulfills the Mathematics requirements by following one of the programs listed above for a Double Major with Mathematics as the primary subject.

Note: Students will not receive credit for taking MATH 1115.03 after receiving credit for .03, MATH 1500X, or .03.

Minor in Mathematics

This minor is available to students registered in a 120 credit hour Bachelor of Applied Computer Science, Bachelor of Arts, Bachelor of Commerce, Bachelor of Community Design, Bachelor of Computer Science, Bachelor of Informatics, Bachelor of Management, Bachelor of Music, Bachelor of Science or Bachelor of Science (Medical Sciences) program.

BA or BScÌý(90 credit hour) degree program with a Minor in Mathematics is also available.

Requirements

* A minimum of 18 credit hours in MATH courses at the 2000 level or higher to a maximum of 36 credit hours.

* It is recommended that students take and .Ìý These are prerequisites for many other upper-level MATH courses.

Contact for more information.

BSc (90 credit hour) Minor in Mathematics

The 90 credit hour Minor in Mathematics is appropriate for students who want to study some Mathematics but do not wish to complete the conventional four-year program. The degree is best suited for students who want a general science degree with some specialization in Mathematics. A 90 credit hour degree program is not suitable for students who wish to pursue graduate studies. With additional study, the degree may be upgraded to a 120 credit hour Major or Honours degree at a later date.

A 90 credit hour BSc in Mathematics is usually the preferred option for students who wish to combine studies in Mathematics with a degree in Engineering (see BSc/BEng Concurrent Program).

See theÌýÌýsection of this Calendar.

Co-op, Minors, Certificates and Engineering Concurrent Programs for Students

Minors available to students in Mathematics

Minor programs allow students to develop subject specialties in addition to their Major or Honours subjects. Minors in other subjects are normally added to 120 credit hour BSc or BA programs (including Science Co-op).

Students in a BSc (120 credit hour) program in Mathematics may choose to include a Minor selected from theÌý. Courses counted toward a Major or Honours subject cannot be used to fulfill the requirements of a Minor program.

Certificates

In combination with a BSc in Mathematics, students may obtain one or more Certificates. A Certificate indicates that a student has achieved a certain level of proficiency in a given area or subspecialty. Courses counted toward a Major, Honours or Minor subject may also be used to fulfill the requirements of a Certificate. Students must apply to the Certificate Coordinator to be considered for a Certificate. Certificates are awarded upon graduation and are noted on the student’s academic transcript.

A complete list of and requirements can be found at the beginning of the section. Students may also work toward obtaining Certificates offered by other Faculties; some of these are listed in the section of the calendar.

Certificates of particular interest to students enrolled in a BSc in Mathematics include:

BSc/BEng Concurrent Program

BEng/BSc (90 credit hour) concurrent degree (Mathematics)

This degree combines an engineering degree with a deeper knowledge of mathematics, and provides a strong foundation for students interested in areas such as robotics, telecommunications, systems analysis and modelling. Following is the recommended sequence of courses for students wishing to obtain a concurrent BEng and BSc (90 credit hour) degree with Minor in Mathematics. Interested students must consult with the Assistant Dean, Faculty of Science, and the Associate Dean, Faculty of Engineering prior to enrolling in a concurrent BEng/BSc degree.Ìý

It is recommended that students also discuss their selection of courses with an undergraduate advisor in the Department of Mathematics and Statistics. A concurrent BEng/BSc Honours Mathematics program can be designed for interested candidates.

Ìý

^a To meet the BSc 90 credit hour Minor in Mathematics requirements, students complete 30 credit hours in addition to their Engineering requirements: 12 credit hours of MATH courses at or above the 2000 level, as specified above, 6 MATH credit hours at or above the 3000 level, 6 credit hours of social science/humanities courses, and 6 credit hours in Science/FASS courses (which may be MATH)

^b Writing requirement: choose from eligible writing courses in CLAS, ENGL, GERM, HIST, PERF, PHIL, RELS, or RUSN to fulfill writing and humanities requirements [College of Arts and Science]

^c Choose from CANA, CTMP, ECON, EMSP, EURO, GWST, HIST, HSTC, INTD, POLI, PSYO, SOSA, SUST for social science courses. Choose from ARBC, CANA, CHIN, CLAS, CTMP, CRWR, EMSP, EURO, SWST, GERM, HIST, HTSC, ITAL, PERF, PHIL, RELS, RUSN, SPAN and THEA for humanities courses

^dÌý See Engineering section of the calendar for details

^e Upper level courses that may be of particular interest to Engineering students include , and

Notes:

• For a BEng/BSc with Minor in Math, students will not receive credit for , or
• Completion of , and fulfill the Math Minor requirements for and
• fulfills the requirement for the Math minor

Courses

Below you will find descriptions for courses offered in this field of study.Ìý You will find a general overview of the topics covered and any prerequisite course or grade requirements, credit value and exclusions.

The first digit of the course indicates the general level.Ìý Those in the 1000 series are introductory degree level. Courses at the 2000, 3000, 4000 series are available to students in the second, third, fourth year.Ìý Courses numbered at the 5000 level or above are graduate level.Ìý Courses listed at the 0100 or 0200 series are technology level courses. Courses below the 0100 level are generally non credit courses.

Some courses are listed as exclusionary to one another.Ìý This means that students may not take both courses so designated.Ìý

Not all courses are offered each year.Ìý Please consult the current timetable for this year’s offering.Ìý For further information please contact the department.

Course Notes

Course descriptions for Statistics can be found in the calendar under Statistics.

Credit may not be obtained twice for the same course even if the numbers have been changed.

Courses with the designation (MLC) are supported by the tutorial services of the Math Learning Centre.

The following three courses below the 1000 level are offered by the College of Continuing Education. Students register and pay for them at the College of continuing Education located at 1220 LeMarchant Street, 2nd Floor or by calling (902) 494-2375 (see for more details).