The Department of Mathematics offers opportunities for study leading to doctoral, master's, and bachelor's degrees. For information on the Bachelor of Arts in Mathematics, see Arts Mathematics. For information on advanced degrees, see graduate Mathematics.
Students should note that the first digit in the number of a course is intended to convey the level of mathematical maturity at which the course is conducted rather than the year in which it must be taken.
Co-operative Education
Detailed information is available from the Mathematics Department or Co-operative Education.
Major
The Department offers a large selection of courses in various areas of pure and applied mathematics and requiring various levels of mathematical sophistication. The student is advised to consult a Mathematics advisor during the second year or when considering a Major in Mathematics in order to design a coherent program of study suitable to the student's interests and abilities.
Major (0456): Mathematics (MATH)
| First Year | |
| Communication Requirement1 | 6 |
| MATH_V 100 or 102 or 104 (or 120 or 180 or 184)2,3 | 3 |
| MATH_V 101 or 103 or 105 (or 121)3 | 3 |
| PHYS_V 100-level4 | 3 |
| CPSC_V 110 (or 103 and 107)5 | 4 |
| Electives6 | 11 |
| Total Credits | 30 |
| Second Year | |
| MATH_V 200 (or 226)7 | 3 |
| MATH_V 2207 | 3 |
| MATH_V 221 (or 223), 2158 | 6 |
| CPSC_V 210 or MATH_V 210 3,9 | 3 |
| Electives6 | 15 |
| Total Credits | 30 |
| Third and Fourth Years | |
| MATH_V courses numbered 300 or higher10 | 24 |
| MATH_V, STAT_V, or CPSC_V courses numbered 300 or higher | 6 |
| Electives6 | 30 |
| Total Credits | 60 |
| Total Credits for Degree | 120 |
| 1 A total of 6 credits of coursework is required to meet the Communication Requirement. For a full list of acceptable courses see Communication Requirement. | |
| 2 See UBC-SFU-UVIC-UNBC Calculus Examination Certificate. Also, MATH_V 110 may substitute for any of the specified courses by decreasing the electives in any year by 3 credits. | |
| 3 A 4-credit course may substitute for a 3-credit course to satisfy a specified requirement by decreasing the electives in any year by 1 credit. | |
| 4 Chosen from 100-level PHYS_V courses, excluding PHYS_V 100. Students who do not have B.C. High School Physics 12 (or equivalent) must take PHYS_V 100 before taking other 100-level PHYS_V courses. Qualified students are encouraged to take PHYS_V 107. | |
| 5 A 6-credit combination of two courses may substitute for a 4-credit course to satisfy the specified requirement by decreasing the electives in any year by 2 credits. | |
| 6 Students are permitted to move elective credits between years. Elective credits together with required courses must fulfill the Faculty of Science’s: a) Foundational Requirement; b) Laboratory Science Requirement; c) Science Breadth Requirement; d) Science and Arts Requirements; e) Upper-level Requirement; f) General Degree Requirements. | |
| 7 Students obtaining 68% or higher in MATH_V 226 may replace MATH_V 220 with 3 credits of electives. In order to be promoted to third year, students must complete one of MATH_V 220, 226. | |
| 8 MATH_V 215 may be deferred until third year. | |
| 9 MATH_V 210 may not be offered every year. | |
| 10 STAT_V 302 can substitute for MATH_V 302. | |
Recommendations
The Department makes the following recommendations:
- Mathematically able students are encouraged to take the honours stream MATH_V 120, 121, 223, 226, and 227.
- In second year, MATH_V 221 should be taken in Term 1. It is possible to take (with appropriate prerequisites) some of MATH_V 307, 308, 312, 317, 340, and MATH_V/STAT_V 302 (as well as MATH_V 300) in the second year.
- Students interested in pursuing statistics to some depth should take STAT_V 200 and MATH_V/STAT_V 302 in the second year. This will prepare them for more advanced statistics courses such as STAT_V 305, 306, and 404.
- Major students should consider taking some of MATH_V 300, 320, 322.
- MATH_V 302 and MATH_V 307 are courses which are useful in many areas of mathematics.
- Students interested in operations research should take MATH_V 340, 441, 442, and 443. They are also advised to take MATH_V 303, STAT_V 305, and 306, and some advanced computer science courses.
- Students interested in teaching are advised to take MATH_V 308, 309, 312, 313, 414, 446.
- Students interested in becoming actuaries can make substantial progress toward this career goal while majoring in mathematics or statistics. These students should consult the actuarial advisors in the Mathematics and/or Statistics Departments for detailed advice on course selection and advice on taking the Society of Actuaries' exams.
- Students interested in the physical sciences should take MATH_V 317 which is important for MATH_V 300, 316.
- Students interested in economics should consider taking ECON_V 420 and 421, and should consult an advisor in the Vancouver School of Economics for other appropriate economics courses. A joint Major in Mathematics and Economics is available. See below.
- In selecting electives, students should consider pursuing an area of application of mathematics in some depth. They should also ensure that they fulfill all the graduation requirements of the Faculty of Science.
Major in Mathematical Sciences
The Major in Mathematical Sciences is offered with Departments of Computer Science and Statistics.
Major (0185): Mathematical Sciences (MASC)
| First Year | |
| Communication Requirement1 | 6 |
| CPSC_V 110 (or 103 and 107)2 | 4 |
| CPSC_V 121 | 4 |
| DSCI_V 100 | 3 |
| MATH_V 100 or 102 or 104 (or 120 or 180 or 184)3,4 | 3 |
| MATH_V 101 or 103 or 105 (or 121)4 | 3 |
| PHYS_V 100-level5 | 3 |
| Electives6 | 4 |
| Total Credits | 30 |
| Second Year | |
| CPSC_V 210, 213, 221 | 12 |
| MATH_V 200 (or 2267), 221 (or 223) | 6 |
| MATH_V 2207 | 3 |
| MATH_V/STAT_V 302 | 3 |
| STAT_V 200, 201 | 6 |
| Total Credits | 30 |
| Third and Fourth Years | |
| Three courses from CPSC_V 302, 303, 320, 340, 402, 406, 420, 421 | 9 |
| Three courses from MATH_V 215, 3038, 307, 340 | 9 |
| STAT_V 305, 306 | 6 |
| Two additional courses from CPSC_V 302, 303, 320, 340, 402, 406, 420, 421, MATH_V 215, 3038, 307, 340, STAT_V 404, 406, 443 | 6 |
| Electives6 | 30 |
| Total Credits | 60 |
| Total Credits for Degree | 120 |
| 1 A total of 6 credits of coursework is required to meet the Communication Requirement. For a full list of acceptable courses see Communication Requirement. | |
| 2 While CPSC_V 110 is the recommended route for students pursuing a specialization in Computer Science, CPSC_V 103, 107 may be taken in its place by decreasing the electives in any year by 2 credits. | |
| 3 See UBC-SFU-UVIC-UNBC Calculus Examination Certificate. Also, MATH_V 110 may substitute for any of the specified courses by decreasing the electives in any year by 3 credits. | |
| 4 A 4-credit course may substitute for a 3-credit course to satisfy a specified requirement by decreasing the electives in any year by 1 credit. | |
| 5 Chosen from 100-level PHYS_V courses, excluding PHYS_V 100. Students who do not have B.C. High School Physics 12 (or equivalent) must take PHYS_V 100 before taking other 100-level PHYS_V courses. Qualified students are encouraged to take PHYS_V 107. | |
| 6 Students are permitted to move elective credits between years. Elective credits together with required courses must fulfill the Faculty of Science’s: a) Foundational Requirement; b) Laboratory Science Requirement; c) Science Breadth Requirement; d) Science and Arts Requirements; e) Upper-level Requirement; f) General Degree Requirements. | |
| 7 Students obtaining 68% or higher in MATH_V 226 may replace MATH_V 220 with 3 credits of electives. In order to be promoted to third year, students must complete one of MATH_V 220, 226. | |
| 8 MATH_V 418 may be substituted for MATH_V 303. | |
Combined Major (1135): Mathematics and Economics (MATH, ECON)
Students interested in the Combined Major must be accepted to the specialization by both the Department of Mathematics and the Vancouver School of Economics. To enter the specialization, students first apply to be admitted as a major in mathematics for second year by using the online process administered by the Faculty of Science. Then they enrol in the courses for the Combined Major for second year. Near the end of second year, they apply in writing to the Vancouver School of Economics. The minimum requirements for admission are the same as those for the BA Major in Economics. (For details, and to explore the BA Major in Mathematics and Economics, see the listing under the Faculty of Arts.)
| First Year | |
| Communication requirement1 | 6 |
| ECON_V 101, 1022 | 6 |
| MATH_V 100 (or one of 102, 104, 110, 120, 180, 184)3,4 | 3 |
| MATH_V 101 (or one of 103, 105, 121)4 | 3 |
| PHYS_V 100-level5 | 3 |
| CPSC_V 110 (or 103 and 107)6 | 4 |
| Electives7 | 5 |
| Total Credits | 30 |
| Second Year | |
| ECON_V 32510,12 | 3 |
| ECON_V 200- or 300-level8 | 3 |
| MATH_V 200 (or 2268), 215, 2208, 221 (or 223) | 12 |
| CPSC_V 210 or MATH_V 2104,9 | 3 |
| Electives7 | 9 |
| Total Credits | 30 |
| Third and Fourth Years | |
| ECON_V 301, 302, 326, 490 | 12 |
| ECON_V courses numbered 300 or higher | 3 |
| ECON_V courses numbered 400 or higher | 3 |
| MATH_V courses numbered 300 or higher11 | 18 |
| Science courses numbered 300 or higher | 12 |
| Electives7,12 | 12 |
| Total Credits | 60 |
| Total Credits for Degree | 120 |
| 1 A total of 6 credits of coursework is required to meet the Communication Requirement. For a full list of acceptable courses see Communication Requirement. | |
| 2 Students with third-year standing can satisfy this requirement by taking ECON_V 310 and ECON_V 311. | |
| 3 See UBC-SFU-UVIC-UNBC Calculus Examination Certificate. | |
| 4 The first 3 credits of the course selected here will be used to satisfy the requirement. Any remaining credits are treated as electives, and can be used in any year. | |
| 5 Chosen from 100-level PHYS_V courses, excluding PHYS_V 100. Students who do not have B.C. High School Physics 12 (or equivalent) must take PHYS_V 100 before taking other 100-level PHYS_V courses. Qualified students are encouraged to take PHYS_V 106. | |
| 6 A 6-credit combination of two courses may substitute for a 4-credit course to satisfy the specified requirement by decreasing the elective in any year by 2 credits. | |
| 7 Students are permitted to move elective credits between years. Elective credits together with required courses must fulfill the Faculty of Science’s: a) Foundational Requirement; b) Laboratory Science Requirement; c) Science Breadth Requirement; d) Science and Arts Requirements; e) Upper-level Requirement; f) General Degree Requirements. | |
| 8 Students obtaining 68% in MATH_V 226 may replace MATH_V 220 with 3 credits of electives. In order to be promoted to third year, students must complete one of MATH_V 220, 226. | |
| 9 MATH_V 210 may not be offered every year. | |
| 10 Students can earn exemption from ECON_V 325 by completing one of the approved equivalents listed here. | |
| 11 Suitable electives include MATH_V 302, 303, 320, 321, 402, 403, 418, 419, 443. MATH_V 320 would be valuable for graduate study in economics. STAT_V 302 can substitute for MATH_V 302. | |
| 12 The Combined Major requires 30 credits of ECON_V courses. Credits earned in approved non-ECON_V courses used to gain exemption from an ECON_V course do not count toward this requirement. | |
Combined Major (1429): Computer Science and Mathematics
Students admitted to this specialization must satisfy the admission and continuation requirements for majors students in both the Department of Mathematics and the Department of Computer Science.
| First Year | |
| Communication Requirement1 | 6 |
| CPSC_V 110 (or 103 and 107)2 | 4 |
| CPSC_V 1213 | 4 |
| MATH_V 100 or 102 or 104 (or 120 or 180 or 184)4,5 | 3 |
| MATH_V 101 or 103 or 105 (or 121)5 | 3 |
| PHYS_V 100-level6 | 3 |
| Electives7 | 7 |
| Total Credits | 30 |
| Second Year | |
| CPSC_V 2103 | 4 |
| CPSC_V 213, 221 | 8 |
| MATH_V 200 (or 2268) | 3 |
| MATH_V 2208 | 3 |
| MATH_V 221 (or 223), 2159 | 6 |
| Electives7,10 | 6 |
| Total Credits | 30 |
| Third and Fourth Years | |
| CPSC_V 310, 313, 320 | 10 |
| CPSC_V 302 or 303 | 3 |
| One of CPSC_V 402, 406, 420, 421, 44011 | 3 |
| CPSC_V courses numbered 300 or higher12 | 3 |
| CPSC_V courses numbered 400 or higher12 | 3 |
| MATH_V courses numbered 300 or higher13 | 21 |
| Electives7,10 | 17 |
| Total Credits | 60 |
| Total Credits for Degree | 120 |
| 1 A total of 6 credits of coursework is required to meet the Communication Requirement. For a full list of acceptable courses see Communication Requirement. | |
| 2 While CPSC_V 110 is the recommended route for students pursuing a specialization in Computer Science, CPSC_V 103, 107 may be taken in its place by decreasing the electives in any year by 2 credits. | |
| 3 Students pursuing a Co-op option are advised to add CPSC_V 210 to their course selections in first year. | |
| 4 See UBC-SFU-UVIC-UNBC Calculus Examination Certificate. Also, MATH_V 110 may substitute for any of the specified courses by decreasing the electives in any year by 3 credits. | |
| 5 A 4-credit course may substitute for a 3-credit course to satisfy a specified requirement by decreasing the electives in any year by 1 credit. | |
| 6 Chosen from 100-level PHYS_V courses, excluding PHYS_V 100. Students who do not have B.C. High School Physics 12 (or its equivalent) must take PHYS_V 100 before taking other 100-level PHYS_V courses. Qualified students are encouraged to take PHYS_V 107. | |
| 7 Students are permitted to move electives credits between years. Elective credits together with required courses must fulfill the Faculty of Science’s: a) Foundational Requirement; b) Laboratory Science Requirement; c) Science Breadth Requirement; d) Science and Arts Requirements; e) Upper-level Requirement; f) General Degree Requirements. | |
| 8 Students obtaining 68% or higher in MATH_V 226 may replace MATH_V 220 with 3 credits of electives. In order to be promoted to third year, students must complete one of MATH_V 220, 226. | |
| 9 MATH_V 215 may be deferred until third year. | |
| 10 STAT_V 200 is recommended. | |
| 11 Students electing to take CPSC_V 440 should note that it has CPSC_V 340 as prerequisite. | |
| 12 Credits gained from undergraduate Student-Directed Seminars (CPSC_V 490) cannot be used to fulfill this requirement. | |
| 13 STAT_V 302 can be substituted for MATH_V 302. | |
Dual Degree Program in Mathematics and Education
The Dual Degree program in Mathematics and Education offers qualified students the opportunity to earn a B.Sc. degree in Mathematics (Major) and a B.Ed. degree in Secondary Education, in five winter sessions with some academic requirements in Term 1 of the Summer sessions. After completing all the requirements, students are normally eligible for a British Columbia Professional Teaching Certificate. Admission to the Dual Degree program requires application in the fall of second year and successful completion of a teaching practicum at the end of second year. See the Dual Degree Program in Science and Education for more information on admission and continuation requirements.
Dual Degree Program: B.Sc. (Mathematics), B.Ed. (Secondary)
| First Year (Winter) | |
| Communication Requirement1,2 | 6 |
| CPSC_V 110 (or 103 and 107)3 | 4 |
| MATH_V 100 or 102 or 104 (or 120 or 180 or 184)4,5 | 3 |
| MATH_V 101 or 103 or 105 (or 121)5 | 3 |
| PHYS_V 100-level6 | 3 |
| Electives3,4,5,7,8 | 11 |
| Total Credits8 | 30 |
| Second Year (Winter) | |
| MATH_V 200 (or 226)9 | 3 |
| MATH_V 2209 | 3 |
| MATH_V 221 (or 223), 21510 | 6 |
| CPSC_V 210 or MATH_V 2105,11 | 3 |
| Electives3,4,5,7,8 | 15 |
| Total Credits1,5 | 30 |
| Second Year (Summer) | |
| EDUC_V 31912 | 1 |
| Total Credits | 1 |
| Third Year (Winter) | |
| EDST_V 401 | 3 |
| LLED_V 360 | 3 |
| MATH_V courses numbered 300 or higher13 | 15 |
| Electives3,4,5,7,8 | 9 |
| Total Credits | 30 |
| Third Year (Summer) | |
| EDUC_V 39912 | 1 |
| Total Credits | 1 |
| Fourth Year (Winter) | |
| EDCP_V 342 | 3 |
| EPSE_V 308 | 4 |
| EDCP_V 343 | 3 |
| MATH_V courses numbered 300 or higher13 | 6 |
| MATH_V, STAT_V, or CPSC_V courses numbered 300 or higher | 6 |
| Electives3,4,5,7,8 | 9 |
| Total Credits | 31 |
| Fourth Year (Summer) | |
| LLED_V 361 | 3 |
| EPSE_V 317 | 3 |
| EDST_V 403 | 1 |
| EDST_V 404 | 1 |
| EDUC_V 430 | 1 |
| EDUC_V 440 | 3 |
| Electives3,4,5,7,8,14 | 3 |
| Total Credits | 15 |
| Fifth Year (Winter)15 | |
| EDUC_V 315 | 2 |
| EDUC_V 421 | 12 |
| EDUC_V 450 | 3 |
| EDUC_V 451 | 3 |
| EPSE_V 310 | 3 |
| MATH_V courses numbered 300 or higher13 | 3 |
| Electives3,4,5,7,8 | 3 |
| Total Credits | 29 |
| Fifth Year (Summer) | |
| EDUC_V 45216 | 3 |
| Total Credits | 3 |
| Total Credits for Dual Degree | 170 |
| 1 A total of 6 credits of coursework is required to meet the Communication Requirement. For a full list of acceptable courses see Communication Requirement. | |
| 2 The Faculty of Education does not accept SCIE_V 113 or APSC_V 176 to meet their English requirement, but they do accept ASTU_V 100, ASTU_V 150, WRDS_V 150 to be equivalent to ENGL_V 112. However students are required to take a minimum of 3 credits of literature coursework from ENGL_V 100, 110, 111, 120, 121. Some of the acceptable courses are not available for students enrolled in the Faculty of Science but might have already been taken by students that transferred to the Faculty of Science. | |
| 3 A 6-credit combination of two courses may substitute for a 4-credit course to satisfy a specified requirement by decreasing the electives in any year by 2 credits. | |
| 4 See UBC-SFU-UVIC-UNBC Calculus Examination Certificate. Also, MATH_V 110 may substitute for any of the specified courses by decreasing the electives in any year by 3 credits. | |
| 5 A 4-credit course may substitute for a 3-credit course to satisfy a specified requirement by decreasing the electives in any year by 1 credit. | |
| 6 Chosen from 100-level PHYS_V courses, excluding PHYS_V 100. Students without Physics 12 must take PHYS_V 100 before taking other 100-level PHYS_V courses. Qualified students are encouraged to take PHYS_V 107. | |
| 7 Students are permitted to move elective credits between years. Elective credits together with required courses must fulfill the Faculty of Science’s: a) Foundational Requirement; b) Laboratory Science Requirement; c) Science Breadth Requirement; d) Science and Arts Requirements; e) Upper-level Requirement; f) General Degree Requirements. | |
| 8 Students who earn more than 30 credits in first year may reduce the number of unrestricted electives taken in later years. | |
| 9 Students obtaining 68% or higher in MATH_V 226 may replace MATH_V 220 with 3 credits of electives. In order to be promoted to third year, students must complete one of MATH_V 220, 226. | |
| 10 MATH_V 215 may be deferred until third year. | |
| 11 MATH_V 210 may not be offered every year. | |
| 12 EDUC_V 319 and EDUC_V 399 are one-week and two-week teaching practica respectively during the month of May in Year 2 and Year 3. Successful completion of EDUC_V 319 and EDUC_V 399 are normally required to continue the B.Ed. program. | |
| 13 Must fulfill Faculty of Education breadth requirements (MATH_V 308, 309, 312, 313, 446 recommended). | |
| 14 EDCP_V 441 is a recommended elective in Fourth Year (Summer). | |
| 15 Note that in fifth year, only Term 1 is available for non-education courses because Term 2 includes education courses that preclude time for other courses. | |
| 16 Note that Education may schedule EDUC_V 452 to Fifth Year Winter in order to meet the May convocation deadline. | |
Honours
Students planning to take a Bachelor of Science with Honours in Mathematics, or in Mathematics combined with another subject, should note the following:
- To be admitted into an Honours Mathematics specialization, a student must obtain at least 68% in MATH_V 121 or average at least 80% in 6 credits of 100-level MATH_V courses. In addition, honours students must comply with the Faculty of Science's honours requirements.
- The courses MATH_V 120, 121, 223, 226, and 227 provide a firmer foundation for advanced study than the alternatives shown in parentheses.
- Students are encouraged to choose electives that result in studying another subject to substantial depth.
- For students who plan to work in mathematics, study in French, German, or Russian is recommended.
Honours (0166): Mathematics (MATH)
| First Year | |
| Communication Requirement1 | 6 |
| MATH_V 120 (or 100 or 102 or 104 or 180 or 184)2,3 | 4 |
| MATH_V 121 (or 101 or 103 or 105)3 | 4 |
| PHYS_V 106 (or 107 or 117 or 101 or 131)4 | 3 |
| CPSC_V 110 (or 103 and 107)5 | 4 |
| Electives6 | 12 |
| Total Credits7 | 33 |
| Second Year | |
| MATH_V 223 (or 221) | 3 |
| MATH_V 226 (or 200) 8 | 3 |
| MATH_V 227 (or 317) | 3 |
| MATH_V 2159 | 3 |
| CPSC_V 210 or MATH_V 2103,10 | 4 |
| Electives6 | 17 |
| Total Credits7 | 33 |
| Third and Fourth Years | |
| MATH_V 300, 320, 321, 322, 323 | 15 |
| 15 credits from MATH_V 400-406, 412, 418-428, 433-440, 443, 449, 450 | 15 |
| MATH_V courses numbered 300 or higher11 | 9 |
| Electives6 | 27 |
| Total Credits7 | 66 |
| Total Credits for Degree | 132 |
| 1 A total of 6 credits of coursework is required to meet the Communication Requirement. For a full list of acceptable courses see Communication Requirement. | |
| 2 See UBC-SFU-UVIC-UNBC Calculus Examination Certificate. Also, MATH_V 110 may substitute for any of the specified courses by decreasing the electives in any year by 2 credits. | |
| 3 If any 3-credit MATH_V course is taken in place of a 4-credit course, the missing credit must be made up as electives. | |
| 4 Students who do not have B.C. High School Physics 12 (or its equivalent) must take PHYS_V 100 in addition to any PHYS_V course(s) taken to satisfy the Science Breadth Requirement. | |
| 5 A 6-credit combination of two courses may substitute for a 4-credit course to satisfy the specified requirement by decreasing the electives in any year by 2 credits. | |
| 6 Students are permitted to move extra electives credits between years. Elective credits together with required courses must fulfill the Faculty of Science’s: a) Foundational Requirement; b) Laboratory Science Requirement; c) Science Breadth Requirement; d) Science and Arts Requirements; e) Upper-level Requirement; f) General Degree Requirements. | |
| 7 Honours students must comply with the Faculty of Science's honours requirements. | |
| 8 Students who take MATH_V 200 or who obtain less than 68% in MATH_V 226 must take MATH_V 220 and obtain 80% or higher in order to take the required course MATH_V 320. | |
| 9 MATH_V 215 may be deferred until third year. | |
| 10 MATH_V 210 may not be offered every year. | |
| 11 STAT_V 302 can substitute for MATH_V 302. | |
Combined Honours (0206): Chemistry and Mathematics
See Chemistry.
Combined Honours (0021): Computer Science and Mathematics
See Computer Science.
Combined Honours (0014): Physics and Mathematics
See Physics.
Combined Honours (0550): Mathematics and Statistics
See Statistics.
Combined Honours: Mathematics (MATH) with Another Subject
| First Year | |
| Same as Mathematics Honours. | |
| Second Year | |
| Same as Mathematics Honours. | |
| Third and Fourth Years | |
| MATH_V 320, 321 | 6 |
| 9 credits from MATH_V 300, 301, 316, 322, 323, 331 | 9 |
| 12 credits from MATH_V 400-406, 412, 418-428, 433-440, 443, 449, 450 | 12 |
| Electives1 | 39 |
| Total Credits2 | 66 |
| Total Credits for Degree | 132 |
| 1 Including courses as specified by the other department, but not exceeding 30 credits in third and fourth year. | |
| 2 Honours students must comply with the Faculty of Science's honours requirements. | |