The following includes York University Undergraduate Programmes Calendar copy updated for 1995/96. Additional changes for implementation in 1995/96 will be added as they are approved. For requirements for BA programmes in Mathematics and Statistics, consult the 1993/94 York University Undergraduate Programmes Calendar and the 1994/95 Supplement to that Calendar. updated 1995 02 14 FACULTY OF PURE AND APPLIED SCIENCE ... V. PROGRAMME OF STUDY REQUIREMENTS OF HONOURS AND ORDINARY PROGRAMMES APPLIED MATHEMATICS See Mathematics and Statistics. ... MATHEMATICS AND STATISTICS The Department of Mathematics and Statistics offers BSc degree programmes in three major subjects: I. Applied Mathematics II. Mathematics III. Statistics The degree programmes in each major are listed separately below. A student should choose one of these majors based on interest and employment goals, but it is possible to change majors provided the requirements of the desired major can be met. i) All BSc degree candidates must complete a programme core (see programme specifications below). ii) All candidates must comply with general regulation 4 (section IV, page ##) by completing the following (in addition to 1000- level COSC and MATH requirements): o 12 credits from SC/BIOL1010.06, SC/CHEM1010.06, SC/EATS1010.06, SC/PHYS1410.06 or SC/PHYS1010.06; o 6 credits in each of Humanities and Social Science (no substitutions permitted). iii) All degree candidates, in accordance with their declared programmes, must comply with general regulation 5 or 6 (section IV, page ##) and, in so doing, must satisfy the course, credit and standing requirements specified below. To declare Honours requires successful completion of at least 24 credits and a minimum cumulative credit-weighted grade-point average of 5.0 over all Science (SC) courses completed. To proceed in each year of an Honours BSc programme requires a minimum cumulative credit-weighted grade-point average of 5.0 over all Science (SC) courses completed. To graduate in an Honours BSc programme requires successful completion of all Faculty requirements and departmental required courses and a minimum cumulative credit-weighted grade-point average of 5.0 over all Science (SC) courses completed. Notes: 1. All candidates beyond the 1000 level must obtain written approval of their study lists from an authorized member of the Department of Mathematics and Statistics. 2. For the purpose of satisfying departmental degree requirements, the following minimum numbers of credits must be completed within the Department of Mathematics and Statistics: 18 for the Ordinary Programme, 21 for the Combined Honours Programme, 30 for the Specialized Honours Programme. 3. For BA degree programmes in Mathematics and Statistics, see the Faculty of Arts section in this Calendar. I. APPLIED MATHEMATICS BSc PROGRAMMES All degree candidates must complete the programme core: SC/COSC1540.03; SC/MATH1013.03 or SC/MATH1000.03; SC/MATH1014.03 or SC/MATH1010.03; SC/MATH1025.03; SC/MATH2015.03; SC/MATH2030.03; SC/MATH2041.03; SC/MATH2042.03; SC/MATH2222.03; SC/MATH2270.03; SC/MATH3241.03; SC/MATH3242.03. In addition, all degree candidates must select, from the Group A and Group B lists below, the number of credits required for their chosen programme. Group A: SC/MATH1090.03, SC/MATH2090.03, SC/MATH2280.03, SC/MATH2320.03, SC/MATH3110.03, SC/MATH3170.06, SC/MATH3260.03, SC/MATH3270.03, SC/MATH3271.03, SC/MATH3272.03, SC/MATH3280.06, SC/MATH3410.03, SC/MATH3440.03, SC/MATH4000.06 (4000.03) (projects in Applied Mathematics only), SC/MATH4141.03, SC/MATH4142.03, SC/MATH4160.03, SC/MATH4170.06, SC/MATH4210.03, SC/MATH4240.03, SC/MATH4241.03, SC/MATH4270.03, SC/MATH4280.03, SC/MATH4430.03, SC/MATH4470.03, SC/MATH4830.03 Group B: SC/MATH1131.03, SC/MATH1132.03, SC/MATH3030.03, SC/MATH3131.03, SC/MATH3132.03, SC/MATH3230.03 or SC/MATH3034.03, SC/MATH3330.03 or SC/MATH3033.03 Note: Some sections of SC/MATH4200.06 (4200.03) may be included in Group A or Group B at the discretion of the department. ORDINARY PROGRAMME o the programme core; o at least 9 additional credits at the 3000 level or higher from groups A and B (above), including no more than 6 credits from Group B, for an overall total of at least 42 credits from major SC/MATH courses; o additional elective credits as required for an overall total of at least 90 credits, including at least 66 credits from Science courses and at least 18 credits at the 3000 or higher level. SPECIALIZED HONOURS PROGRAMME o the programme core; o SC/MATH3110.03 (not required if SC/MATH1010.03 has been completed); SC/MATH3260.03; SC/MATH3410.03; o at least 24 additional credits from groups A and B (above), including no more than 9 credits from Group B and at least 12 credits at the 4000 level; o additional elective credits as required for an overall total of at least 120 credits, including at least 90 credits from Science courses and at least 42 credits at the 3000 or higher level. COMBINED HONOURS PROGRAMME o the programme core; o at least 9 additional credits at the 3000 level or higher from groups A and B (above), including no more than 6 credits from Group B, for an overall total of at least 42 credits from major SC/MATH courses; o additional credits (including those required for the second major) as required for an overall total of at least 120 credits, including at least 90 credits from Science courses and at least 42 credits at the 3000 or higher level. II. MATHEMATICS BSc PROGRAMMES ORDINARY PROGRAMME o SC/COSC1520.03 and SC/COSC1530.03, or equivalents; o SC/MATH1300.03 and SC/MATH1310.03, or equivalents; o SC/MATH1090.03 or SC/MATH2090.03 or SC/MATH2320.03; o SC/MATH2221.03; SC/MATH2222.03; SC/MATH2310.03; o at least 12 credits in major (i.e., without second digit 5) SC/MATH courses, or approved or equivalent courses, at the 3000 level or higher, for a total of at least 30 credits in major SC/MATH courses; o additional elective credits as required for an overall total of at least 90 credits, including at least 66 credits from Science courses and at least 18 credits at the 3000 or higher level. Note: Mathematics Honours Core courses SC/MATH1000.03, SC/MATH1010.03, SC/MATH2010.03, SC/MATH2021.03, and SC/MATH2022.03 may replace SC/MATH1300.03, SC/MATH1310.03, SC/MATH2310.03, SC/MATH2221.03, and SC/MATH2222.03, respectively. HONOURS PROGRAMMES MATHEMATICS HONOURS CORE The core courses below are required in all Honours Mathematics programmes. o SC/COSC1520.03 and SC/COSC1530.03, or equivalents; o SC/MATH1000.03; SC/MATH1010.03; o SC/MATH1090.03 or SC/MATH2090.03 or SC/MATH2320.03; o SC/MATH2010.03; SC/MATH3010.03; o SC/MATH2021.03; SC/MATH2022.03. o SC/MATH3020.06, or both SC/MATH3131.03 and SC/MATH3132.03; o SC/MATH3210.03; o 6 credits from SC/MATH4000.06 (4000.03) (projects in pure mathematics), SC/MATH4010.06, SC/MATH4020.06, SC/MATH4030.03, SC/MATH4080.06, SC/MATH4110.03, SC/MATH4120.03, SC/MATH4130.03, SC/MATH4140.03, SC/MATH4150.03, SC/MATH4160.03, SC/MATH4170.06, SC/MATH4210.03, SC/MATH4230.03, SC/MATH4250.06, SC/MATH4280.03, SC/MATH4290.03, SC/MATH4430.03, SC/MATH4630.03, SC/MATH4730.03. Note: Students may substitute non-Honours versions of the sequence SC/MATH1000/1010/2010, but any student who does not complete SC/MATH1010.03 must take SC/MATH3110.03 above and beyond the normal Honours requirements. If one or more of SC/MATH2021.03 or SC/MATH2022.03 is replaced by other linear algebra courses and if the grades obtained were less than A, then SC/MATH2090.03 or SC/MATH2320.03 must be taken above and beyond the normal Honours requirements. SPECIALIZED HONOURS PROGRAMME o the Mathematics Honours Core; o at least 6 additional credits in major SC/MATH courses at the 4000 level (these must include either SC/MATH4010.06 or SC/MATH4020.06 if neither was taken as part of the Mathematics Honours Core); o at least 24 additional credits in major (i.e., without second digit 5) SC/MATH courses, or approved or equivalent courses, for a total of at least 66 credits in major SC/MATH courses; o additional elective credits as required for an overall total of at least 120 credits, including at least 90 credits from Science courses and at least 42 credits at the 3000 or higher level. COMBINED HONOURS PROGRAMME o the Mathematics Honours Core, for a total of at least 36 credits in major SC/MATH courses. o additional credits (including those required for the second major) as required for an overall total of at least 120 credits, including at least 90 credits from Science courses and at least 42 credits at the 3000 or higher level. III. STATISTICS BSc PROGRAMMES ORDINARY PROGRAMME o SC/COSC1520.03 and SC/COSC1530.03, or SC/COSC1540.03, or SC/COSC1020.03 and SC/COSC1030.03, or equivalents; o 6 credits from 1000-level major (i.e., without second digit 5) SC/MATH courses in calculus; o SC/MATH1131.03; SC/MATH1132.03; SC/MATH2030.03; o SC/MATH2221.03 or SC/MATH1025.03 or SC/MATH2021.03; SC/MATH2222.03 or SC/MATH2022.03; o SC/MATH2310.03, or SC/MATH2015.03, or SC/MATH2010.03 and SC/MATH3010.03; o SC/MATH3033.03; SC/MATH3131.03; o at least 3 credits from SC/MATH3034.03, SC/MATH3132.03, SC/MATH3430.03, SC/MATH4130.03, SC/MATH4230.03, SC/MATH4630.03, SC/MATH4730.03, SC/MATH4830.03, SC/MATH4930.03, for a total of at least 33 credits in major SC/MATH courses; o additional elective credits as required for an overall total of at least 90 credits, including at least 66 credits from Science courses and at least 18 credits at the 3000 or higher level. Note: A student may substitute SC/MATH2560.03 and SC/MATH2570.03 with an average of B+ or higher for SC/MATH1131.03 and SC/MATH1132.03. SPECIALIZED HONOURS PROGRAMME o SC/COSC1520.03 and SC/COSC1530.03, or SC/COSC1540.03, or SC/COSC1020.03 and SC/COSC1030.03, or equivalents; o SC/MATH1000.03; SC/MATH1010.03; o SC/MATH1131.03; SC/MATH1132.03; o SC/MATH2010.03; o SC/MATH2021.03; SC/MATH2022.03; o SC/MATH2030.03; o SC/MATH3010.03; SC/MATH3210.03; o SC/MATH3033.03; SC/MATH3034.03; SC/MATH3131.03; SC/MATH3132.03; SC/MATH3430.03; o 6 credits from SC/MATH4130.03 (more than one version may be taken for credit), SC/MATH4230.03, SC/MATH4630.03, SC/MATH4730.03, SC/MATH4830.03, SC/MATH4930.03 (more than one version may be taken for credit); o 6 additional credits from the above or from SC/MATH4030.03, SC/MATH4170.06, SC/MATH4280.03, SC/MATH4430.03; o 9 additional credits from any major (second digit not 5) SC/MATH courses, for a total of at least 66 credits in major SC/MATH courses; o additional elective credits as required for an overall total of at least 120 credits, including at least 90 credits from Science courses and at least 42 credits at the 3000 or higher level. COMBINED HONOURS PROGRAMME o SC/COSC1520.03 and SC/COSC1530.03, or SC/COSC1540.03, or SC/COSC1020.03 and SC/COSC1030.03, or equivalents; o 6 credits from 1000-level major (i.e., without second digit 5) SC/MATH courses in calculus; o SC/MATH1131.03; SC/MATH1132.03; SC/MATH2030.03; o SC/MATH2010.03 and SC/MATH3010.03, or SC/MATH2015.03, or SC/MATH2310.03; o SC/MATH2021.03 or SC/MATH2221.03 or SC/MATH1025.03; SC/MATH2022.03 or SC/MATH2222.03; o SC/MATH3131.03; o 12 credits from SC/MATH3033.03, SC/MATH3034.03, SC/MATH3132.03, SC/MATH3430.03, SC/MATH4130.03 (more than one version may be taken for credit), SC/MATH4230.03, SC/MATH4630.03, SC/MATH4730.03, SC/MATH4830.03, SC/MATH4930.03 (more than one version may be taken for credit), for a total of at least 39 credits in major SC/MATH courses. o additional credits (including those required for the second major) as required for an overall total of at least 120 credits, including at least 90 credits from Science courses and at least 42 credits at the 3000 or higher level. ... STATISTICS See Mathematics and Statistics. ... COURSES OF INSTRUCTION YORK CAMPUS ... APPLIED MATHEMATICS - PURE AND APPLIED SCIENCE, ARTS See Mathematics and Statistics. ... MATHEMATICS AND STATISTICS - ARTS, PURE AND APPLIED SCIENCE, ATKINSON COLLEGE Department Office: N520 Ross, 736-5250 Associate Professor and Chair of the Department: G.A. Monette Professors Emeriti: L. Lorch, D.C. Russell, A. Shenitzer Professors: M. Abramson, R.G. Burns, A. Dow, J. Fox, D.A.S. Fraser, S. Guiasu, C. Hruska, A. Karrass, I. Kleiner, S. Kochman, J. Laframboise, J. Liu, R.P. McEachran, M.E. Muldoon, G.L. O'Brien, P. Olin, J. Wick Pelletier, S.D. Promislow, T. Salisbury, D. Solitar, A.D. Stauffer, J. Steprans, P.A. Taylor, W. Tholen, S. Watson, W.J. Whiteley, M.W. Wong Associate Professor Emeritus: J.H. Grant Associate Professors: D.W.T. Bean, J.-C. Bouhenic, J.M.N. Brown, R.L.W. Brown, K. Bugajska, C. Czado, G.E. Denzel, R.A. Ganong, S.W. Lee, T. MacHenry, N.N. Madras, K.R. Maltman, H. Massam, D.H. Pelletier, P.H. Peskun, A. Pietrowski, N. Purzitsky, P. Rogers, R.A. Schaufele, A.M.K. Szeto, D. Tanny, A. Weiss, J. Wu Assistant Professors: N. Bergeron, S.R. Chamberlin, E.J. Janse van Rensburg, Y. Wu NSERC University Research Fellows: N.N. Madras, K.R. Maltman NSERC Women's Faculty Awardee: F. Vinette The Department of Mathematics and Statistics offers a wide range of courses in both pure and applied mathematics and statistics. These meet the needs of students who wish to major in mathematics or statistics as well as those who require some knowledge of mathematics or statistics in other disciplines. In addition, there are courses for those who have a general interest in these subjects. Actuarial Profession. Students interested in the actuarial profession should consult the Department of Mathematics and Statistics for guidance. The department will be glad to suggest a programme of courses which will be helpful in preparing for examinations of the Society of Actuaries. Operations Research. The Canadian Operational Research Society (CORS) has recognized that graduation from a programme in Applied Mathematics, Mathematics, or Statistics with a prescribed set of courses will qualify a student for the Diploma in Operations Research awarded by CORS. Interested students should consult the Department of Mathematics and Statistics for guidance. For specific requirements of programmes offered by this department, see page ## for BA programmes and page ## of section V for BSc programmes. COURSES IN MATHEMATICS AND STATISTICS When selecting courses, please note the following: 1. A student taking lower-level mathematics courses may wish to make use of the services provided by the Department's Mathematics Laboratory. 2. AS/SC/MATH1510.06 is intended for students who, despite having one or more OACs in mathematics (or equivalents), have a weak mathematical background. AS/MATH1520.06 is designed for students who do not have credit in any OACs in mathematics. Both AS/SC/MATH1510.06 and AS/MATH1520.06 can serve as preparation for AS/SC/MATH1500.03 and from there entrance to further calculus courses. 3. Note on calculus courses for first-year students. a) BBA students who wish to take only a minimum amount of mathematics should take both AS/MATH1530.03 and AS/MATH1540.03, or AS/MATH1550.06. The prerequisite for these courses is AS/SC/MATH1500.03 or OAC Calculus or equivalent. b) Science students (particularly those majoring in Biology, Geography, Physical Education or Psychology) who do not require other specific calculus courses to satisfy degree requirements or as prerequisites for higher-level courses, may take SC/MATH1505.06 to satisfy the Faculty of Pure and Applied Science 1000-level mathematics requirement. Other students should be guided by paragraphs (c) and (d) below. c) A student with at least one OAC in mathematics or equivalent, but without previous calculus, must begin the study of calculus with AS/SC/MATH1500.03. d) A student with OAC Calculus or equivalent can begin with AS/SC/MATH1000.03 or AS/SC/MATH1013.03 or AS/SC/MATH1300.03 and then take AS/SC/MATH1010.03 or AS/SC/MATH1014.03 or AS/SC/MATH1310.03. 4. Course numbering. Courses with second digit 5 cannot be used to satisfy departmental degree requirements except (i) by students in the Ordinary Mathematics for Commerce Programme; and (ii) by students in other programmes in a few cases as noted in programme descriptions. Unless otherwise specified, courses whose numbers end in ".06" (i.e., 6-credit courses) have three lecture hours per week for two terms, while those whose numbers end in ".03" (i.e., 3-credit courses) have three lecture hours per week for one term. In addition, problem sessions or tutorials are scheduled for many courses. 5. Arts students should note that some Atkinson College courses are out-of-Faculty and there are restrictions on the number of out-of-Faculty courses that may be taken. Science students should note that some Atkinson College courses are out-of-department - see the restrictions in note 2. on page ## of section V. Atkinson College MATH courses which are cross-listed with MATH courses offered by the Faculties of Arts and Pure and Applied Science are identified in the course outlines below. For a list of other Atkinson College courses which are equivalent to and/or degree credit exclusions for MATH courses in this Calendar, Arts students should consult the "Faculty of Arts Degree Credit Exclusion List for Atkinson College Courses," published annually by the Registrar's Office. Science students should consult the "Atkinson Equivalence Table for Science Students" available in the Science Office of Student Programmes beginning in March each year. AS/SC/MATH1000.03 Differential Calculus (Honours Version). Axioms for real numbers, limits, continuity and differentiability. This course covers slightly fewer topics than AS/SC/MATH1300.03, but covers them in greater depth. It should be taken by all those planning an Honours degree in Mathematics or a Specialized Honours degree in Statistics. Prerequisite: AS/SC/MATH1500.03 or OAC Calculus or equivalent. Degree credit exclusions: AS/SC/MATH1013.03, AS/SC/MATH1300.03, SC/MATH1505.06, AS/MATH1530.03, AS/MATH1550.06, SC/ACMS1030.06, SC/ACMS1050.06, AS/ECON1530.03. AS/SC/MATH1010.03 Integral Calculus (Honours Version). Riemann integral, fundamental theorems of calculus, transcendental functions, integration techniques, sequences, series. This course covers fewer topics than AS/SC/MATH1310.03, but covers them in greater depth. It should be taken by all those planning an Honours degree in Mathematics or a Specialized Honours degree in Statistics. Prerequisite: AS/SC/MATH1000.03 or permission of the department. Degree credit exclusions: AS/SC/MATH1014.03, AS/SC/MATH1310.03, SC/MATH1505.06, AS/SC/AK/MATH3110.03, SC/ACMS1030.06, SC/ACMS1050.06. AS/SC/MATH1013.03 Applied Calculus I. The first half of this course deals with differentiation and the second half with integration. Topics include derivatives of algebraic and transcendental functions, indefinite integrals, techniques of integration, the definite integral and its interpretation as an area. Prerequisite: AS/SC/MATH1500.03 or OAC Calculus. Degree credit exclusions: AS/SC/MATH1000.03, AS/SC/MATH1300.03, SC/MATH1505.06, AS/MATH1530.03, AS/MATH1550.06, SC/ACMS1030.06, SC/ACMS1050.06, AS/ECON1530.03. AS/SC/MATH1014.03 Applied Calculus II. Applications of differential and integral calculus (e.g., maxima and minima, areas, volumes of revolution, moments and centroids, etc.), indeterminate forms, improper integrals, Taylor series, simple ordinary differential equations and an introduction to multivariate calculus. Prerequisite(s): One of AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SC/MATH1300.03, or, for non-Science students only, one of AS/MATH1530.03 and AS/MATH1540.03, AS/MATH1550.06, AS/ECON1530.03 and AS/ECON1540.03. Degree credit exclusions: AS/SC/MATH1010.03, AS/SC/MATH1310.03, SC/MATH1505.06, SC/ACMS1030.06, SC/ACMS1050.06. AS/SC/MATH1025.03 Applied Linear Algebra. Topics include polar coordinates in Euclidean 3-space, general matrix algebra, determinants, vector space concepts for Euclidean n-space (e.g., linear dependence and independence, basis, dimension, linear transformations, etc.), an introduction to eigenvalues and eigenvectors. Prerequisite: AS/SC/MATH1525.03 or OAC Algebra and Geometry. Degree credit exclusions: AS/SC/MATH2000.06, AS/SC/MATH2021.03, AS/SC/AK/MATH2221.03, SC/ACMS1020.06, SC/ACMS1050.06. AS/SC/AK/MATH1090.03 Introduction to Sets and Logic (formerly AS/SC/MATH1120.03 - before 1994/95). Sets, functions, relations, induction, proof techniques, logic and logic circuits, basic combinatorics and some basic graph theory. Prerequisite: One OAC in mathematics or equivalent. Degree credit exclusions: AS/SC/MATH1120.03. This course is not open to any student who has taken or is taking any 3000- or higher-level MATH course. AS/SC/MATH1131.03 Introduction to Statistics I. Displaying and describing distributions, basic concepts of time series and growth, relationships between variables, Simpson's paradox and the need for design. Experimental design and sampling design, randomization. Probability models and random variables, mean and variance. Basic laws of probability. Prerequisite: At least one OAC in mathematics is recommended. Degree credit exclusions: AS/SC/AK/MATH2560.03, SC/BIOL3080.03, SC/BIOL3090.03, AS/ECON2500.03, AS/SC/GEOG2420.03, AS/SC/PHED2050.03, AS/SC/PSYC2020.06, AS/SC/PSYC2021.03, AS/SOCI3030.06. Not open to any student who has successfully completed AS/SC/MATH2030.06. AS/SC/MATH1132.03 Introduction to Statistics II. Inference for the binomial, sample mean, central limit theorem, control charts. Confidence intervals, tests and decisions. Abuses of tests. Comparing two means, inference for spread. Contingency tables. Simple regression and basic analysis of variance. Prerequisite: AS/SC/MATH1131.03. Degree credit exclusions: AS/SC/AK/MATH2570.03, SC/BIOL3080.03, SC/BIOL3090.03, AS/ECON3210.03, AS/ECON3500.03, AS/SC/GEOG2420.03, AS/SC/PHED2050.03, AS/SC/PSYC2020.06, AS/SC/PSYC2022.03, AS/SOCI3030.06. Not open to any student who has successfully completed AS/SC/MATH2030.06. AS/SC/MATH1300.03 Differential Calculus with Applications. Limits, derivatives with applications, antiderivatives, fundamental theorem of calculus, beginnings of integral calculus. Prerequisite: AS/SC/MATH1500.03 or OAC Calculus or equivalent. Degree credit exclusions: AS/SC/MATH1000.03, AS/SC/MATH1013.03, SC/MATH1505.06, AS/MATH1530.03, AS/MATH1550.06, SC/ACMS1030.06, SC/ACMS1050.06, AS/ECON1530.03. AS/SC/MATH1310.03 Integral Calculus with Applications. Transcendental functions, differential equations, techniques of integration, improper integrals, infinite series. Offered in both terms. Prerequisite(s): One of AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SC/MATH1300.03, or, for non-Science students only, one of AS/MATH1530.03 and AS/MATH1540.03, AS/MATH1550.06, AS/ECON1530.03 and AS/ECON1540.03. Degree credit exclusions: AS/SC/MATH1010.03, AS/SC/MATH1014.03, SC/MATH1505.06, SC/ACMS1030.06, SC/ACMS1050.06. AS/SC/MATH1500.03 Introduction to Calculus. Elements of differential calculus, anti-derivatives and integrals, with applications. Designed for students who have not taken (or have performed inadequately in) OAC Calculus. Prerequisite: AS/SC/MATH1510.06 or AS/MATH1520.06 or equivalent. This course may be taken at the same time as the second half of AS/SC/MATH1510.06 or AS/MATH1520.06. Degree credit exclusion: May not be taken by any student who has taken or is currently taking another university course in calculus. SC/MATH1505.06 Mathematics for the Life and Social Sciences. A presentation of the elements of single-variable differential and integral calculus, elementary linear algebra and introductory probability and statistics. This course is designed to provide a comprehensive mathematical background for (Science) students of the biological and social sciences. Emphasis is placed on basic mathematical skills and their applications. Prerequisite: At least one OAC in mathematics or AS/SC/MATH1510.06. Degree credit exclusions: AS/SC/MATH1000.03, AS/SC/MATH1010.03, AS/SC/MATH1013.03, AS/SC/MATH1014.03, AS/SC/MATH1300.03, AS/SC/MATH1310.03, AS/MATH1530.03, AS/MATH1540.03, AS/MATH1550.06, SC/ACMS1020.06, SC/ACMS1030.06, SC/ACMS1050.06, AS/ECON1530.03, AS/ECON1540.03. AS/SC/MATH1510.06 Fundamentals of Mathematics. Designed for the student whose mathematical background is weak and who wishes to take further courses in mathematics. Topics include algebraic equations and inequalities; simple sequences and series; analytic geometry; trigonometry; functions, including algebraic, exponential, logarithmic and trigonometric functions. Degree credit exclusions: AS/MATH1520.06, SC/ACMS1530.06. May not be taken by any student who has taken or is currently taking another university course in mathematics or statistics except for AS/SC/MATH1500.03 and AS/SC/MATH1525.03. AS/MATH1520.06 Fundamentals of Mathematics. Designed for the student whose mathematical background is weak and who wishes to gain some familiarity with mathematical techniques. Topics include algebraic equations and inequalities, simple sequences and series, analytic geometry, sets and functions, the binomial theorem. This course is given on a modularized, self-paced basis through the Department's Mathematics Laboratory. Degree credit exclusions: AS/SC/MATH1510.06, SC/ACMS1530.06. May not be taken by any student who has taken or is currently taking another university course in mathematics or statistics except for AS/SC/MATH1500.03 and AS/SC/MATH1525.03. AS/SC/MATH1525.03 Elementary Linear Algebra. This course is designed for students who have not taken OAC Algebra and Geometry. Topics include complex numbers, mathematical induction, rudiments of linear algebra in the context of Euclidean 2-space and 3-space; e.g., vectors, equations of lines and planes, matrices and linear transformations. Degree credit exclusion: May not be taken by any student who has taken or is taking another university course involving linear algebra. AS/MATH1530.03 Introductory Mathematics for Economists I. This course introduces and develops topics in differential calculus, integral calculus, and their applications in economics. This course or equivalent is required for all Economics majors or minors; it also satisfies the mathematics requirement for the Faculty of Administrative Studies. It is suitable for Ordinary Mathematics for Commerce and for a minor in Statistics, but should not be taken by those who intend to major in any other Mathematics or Statistics programme or in Computer Science. (Same as AS/ECON1530.03.) Offered in both terms. Prerequisite: AS/SC/MATH1500.03 or OAC Calculus or equivalent. Prerequisite or corequisite: AS/ECON1000.03 or AS/ECON1010.03. Degree credit exclusions: AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SC/MATH1300.03, SC/MATH1505.06, AS/MATH1550.06, SC/ACMS1030.06, SC/ACMS1050.06, AS/ECON1530.03. AS/MATH1540.03 Introductory Mathematics for Economists II. This course introduces and develops topics, including matrix algebra, optimization, comparative statics of general function models, and their applications in economics. This course or equivalent is required for all Economics majors or minors; it also satisfies the mathematics requirement for the Faculty of Administrative Studies. (Same as AS/ECON1540.03.) Offered in both terms. Prerequisite: One of AS/MATH1530.03, AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SC/MATH1300.03, AS/ECON1530.03. Prerequisite or corequisite: AS/ECON1000.03 or AS/ECON1010.03. Degree credit exclusions: SC/MATH1505.06, AS/MATH1550.06, SC/ACMS1020.06, SC/ACMS1050.06, AS/ECON1540.03. May not be taken by any student who has taken or is taking AS/SC/MATH1025.03, AS/SC/MATH2000.06, AS/SC/MATH2021.03, AS/SC/AK/MATH2221.03, or equivalent. AS/MATH1550.06 Mathematics with Management Applications. This course is designed to provide a mathematical background for students in the BBA programme. It is also suitable for the Ordinary Programme in Mathematics for Commerce and the minor in Statistics, but should not be taken by those who intend to major in any other programme in Mathematics or Statistics or in Computer Science. It includes calculus, matrix algebra and elements of optimization with applications to management. Prerequisite: AS/SC/MATH1500.03 (may also by taken as a first-term corequisite) or OAC Calculus or equivalent. Degree credit exclusions: AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SC/MATH1300.03, SC/MATH1505.06, AS/MATH1530.03, AS/MATH1540.03, SC/ACMS1030.06, SC/ACMS1050.06, AS/ECON1530.03, AS/ECON1540.03. This course may not be taken by any student who has taken or is taking AS/SC/MATH1025.03 or AS/SC/MATH2000.06 or AS/SC/MATH2021.03 or AS/SC/AK/MATH2221.03 or equivalent. AS/SC/MATH1580.03 The Nature of Mathematics I. Designed to create a positive attitude towards mathematics through an examination of topics relevant to the study of mathematics at the elementary school level. Topics include numeral systems, number theory, nature of algebra and geometry. Intended primarily, but not exclusively, for Education students in the P/J stream. Degree credit exclusion: Not open to any student who has taken or is taking another university mathematics course unless permission of the course coordinator is obtained. AS/SC/MATH1590.03 The Nature of Mathematics II. A continuation of some of the themes explored in AS/SC/MATH1580.03. Further topics include elements of probability and statistics, the nature of computers, elementary set theory and logic. Prerequisite: AS/SC/MATH1580.03 or permission of the course coordinator. AS/SC/MATH2010.03 Vector Differential Calculus. Power series, partial derivatives, linear maps, differentiability of maps from n-space to m-space, chain rule, gradients, tangent lines to curves, tangent planes to surfaces, cross product, implicit function theorem, multidimensional Taylor's theorem with remainder, extrema, quadratic forms, Hessian, Lagrange multipliers. Prerequisite: AS/SC/MATH1010.03 or permission of the department. Degree credit exclusions: AS/SC/MATH2015.03, AS/SC/AK/MATH2310.03. AS/SC/MATH2015.03 Applied Multivariate and Vector Calculus. Topics covered include grad, div, curl and Laplacian in polar coordinates; line and surface integrals; theorems of Gauss and Stokes; double and triple integrals in various coordinate systems; extrema and Taylor series for multivariate functions; differential geometry in Euclidean 3-space. Prerequisite: One of AS/SC/MATH1010.03, AS/SC/MATH1014.03, AS/SC/MATH1310.03, or SC/MATH1505.06 plus permission of the course coordinator. Degree credit exclusions: AS/SC/MATH2010.03, AS/SC/AK/MATH2310.03, AS/SC/MATH3310.03. AS/SC/MATH2021.03 Linear Algebra I (Honours Version). Linear equations, matrices, determinants, vector spaces and inner product spaces. This course covers material similar to that in AS/SC/AK/MATH2221.03 but at a more advanced level. It is required in Honours Mathematics degrees. Prerequisite or corequisite: As prerequisite, one of SC/MATH1505.06, AS/MATH1540.03, AS/MATH1550.06, AS/ECON1540.03; or, as prerequisite or corequisite, one of AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SC/MATH1300.03, or permission of the course coordinator. Degree credit exclusions: AS/SC/MATH1025.03, AS/SC/MATH2000.06, AS/SC/AK/MATH2221.03, SC/ACMS1020.06. AS/SC/MATH2022.03 Linear Algebra II (Honours Version). Linear transformations, eigenvalues, diagonalization, quadratic forms, Markov chains and isometries. This course covers material similiar to that in AS/SC/AK/MATH2222.03 but at a more advanced level. It is required in Honours degrees in Mathematics and in Specialized Honours degrees in Statistics. Prerequisite: AS/SC/MATH2021.03 or permission of the course coordinator. Degree credit exclusions: AS/SC/MATH2000.06, AS/SC/AK/MATH2222.03. AS/SC/AK/MATH2030.03 Elementary Probability (formerly part of AS/SC/MATH2030.06 - before 1993/94). Introduction to the theory of probability as preparation for further study in either mathematical or applied probability and statistics. Topics include probability spaces, conditional probability, independence, random variables, distribution functions, expectation, Chebyshev's inequality, common distributions, moment-generating functions and limit theorems. Prerequisite: One of AS/SC/MATH2015.03, AS/SC/AK/MATH2310.03, AS/SC/MATH2010.03. If a student uses AS/SC/MATH2010.03 as a prerequisite, AS/SC/AK/MATH3010.03 must be taken as a corequisite. Degree credit exclusion: AS/SC/MATH2030.06. AS/SC/MATH2041.03 Symbolic Computation Laboratory I (formerly part of AS/SC/MATH2040.06 - before 1995/96). An introduction to symbolic computing in the Maple environment. Topics from single- variable differential and integral calculus, including simple ordinary differential equations, are covered. Both mathematical understanding and applications are emphasized. Enrolment is limited to 25. Prerequisites: SC/AS/COSC1540.03 or equivalent computing experience; one of AS/SC/MATH1010.03, AS/SC/MATH1014.03, AS/SC/MATH1310.03. Degree credit exclusion: AS/SC/MATH2040.06. AS/SC/MATH2042.03 Symbolic Computation Laboratory II (formerly part of AS/SC/MATH2040.06 - before 1995/96). Advanced symbolic computing with Maple. Topics from linear algebra, differential equations, multivariate calculus, integral theorems, are covered. Both mathematical understanding and applications are emphasized. Enrolment is limited to 25. Prerequisites: AS/SC/MATH2041.03; AS/SC/MATH2010.03 or AS/SC/MATH2015.03 or AS/SC/AK/MATH2310.03; AS/SC/MATH1025.03 or AS/SC/MATH2021.03 or AS/SC/AK/MATH2221.03. Prerequisites or corequisites: AS/SC/AK/MATH2270.03; AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03. Degree credit exclusion: AS/SC/MATH2040.06. AS/SC/MATH2090.03 Introduction to Mathematical Logic. An introduction to propositional logic; predicate logic, with an emphasis on semantics; elements of axiomatic number theory. This course is intended for Computer Science students and for Mathematics students who plan to do further study in logic. Prerequisite: AS/SC/AK/MATH1090.03 or AS/SC/MATH1120.03 or any 2000-level MATH course (without second digit 5) or permission of the course coordinator. AS/SC/AK/MATH2221.03 Linear Algebra with Applications I. Systems of linear equations, linear and affine subspaces of Euclidean n- space, the Gauss-Jordan algorithm, matrices and matrix algebra, determinants, vector space concepts for Euclidean n-space (linear dependence and independence, basis, dimension, etc.), various applications. Prerequisite or corequisite: As prerequisite, one of SC/MATH1505.06, AS/MATH1540.03, AS/MATH1550.06, AS/ECON1540.03; or, as prerequisite or corequisite, one of AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SC/MATH1300.03. Degree credit exclusions: AS/SC/MATH1025.03, AS/SC/MATH2000.06, AS/SC/MATH2021.03, SC/ACMS1020.06. AS/SC/AK/MATH2222.03 Linear Algebra with Applications II. Linear transformations and their representation by matrices, change of basis and similarity, eigenvalues and eigenvectors, diagonalization, inner product spaces, orthogonality, the Gram- Schmidt algorithm, least squares approximations, abstract vector spaces, various applications. Prerequisite: AS/SC/MATH1025.03 or AS/SC/AK/MATH2221.03. Degree credit exclusions: AS/SC/MATH2000.06, AS/SC/MATH2022.03. AS/SC/MATH2260.06 An Introduction to Combinatorics. Basic graph theory, permutations, combinations, inclusion-exclusion principle, recurrence relations, generating functions, occupancy problems, application to probability theory, geometry of the plane, maps on the sphere, colouring problems, finite structures, systems of distinct representatives, existence problems, magic squares, Latin squares. Prerequisite: One OAC in mathematics or equivalent. AS/SC/AK/MATH2270.03 Differential Equations. Introduction to differential equations, including a discussion of the formation of mathematical models for real phenomena; solution by special techniques; applications; linear equations; solutions in series; other topics if time permits. Prerequisites: AS/SC/MATH2010.03 or AS/SC/MATH2015.03 or AS/SC/AK/MATH2310.03; AS/SC/MATH1025.03 or AS/SC/MATH2021.03 or AS/SC/AK/MATH2221.03. AS/SC/MATH2280.03 The Mathematical Theory of Interest. Topics include measurement of interest, annuities, amortization of loans, bonds, sinking funds and depreciation. The course is at a level which will prepare students for the interest theory portion of the Society of Actuaries examinations. Prerequisite: One of AS/SC/MATH1010.03, AS/SC/MATH1014.03, AS/SC/MATH1310.03. Degree credit exclusion: AS/AK/MATH2580.06. AS/SC/AK/MATH2310.03 Calculus of Several Variables with Applications. Vector functions, partial derivatives, gradient, multiple integrals, line integrals, optimization, applications. Offered in both terms. Prerequisite: One of AS/SC/MATH1010.03, AS/SC/MATH1014.03, AS/SC/MATH1310.03. Degree credit exclusions: AS/SC/MATH2010.03, AS/SC/MATH2015.03. AS/SC/MATH2320.03 Discrete Mathematical Structures. This course covers the algebraic and combinatorial structures that are needed in computer science. Topics include set theory, functions, relations, combinatorics, elements of graph theory, posets, lattices, Boolean algebras, moniods, groups, morphisms, congruence relations. Intended primarily, but not exclusively, for students in Computer Science. Prerequisite: AS/SC/AK/MATH1090.03 or AS/SC/MATH1120.03 or any 2000-level MATH course (without second digit 5) or permission of the course coordinator. AS/SC/AK/MATH2560.03 Elementary Statistics I. Displaying and describing distributions, normal distibution. Relationships between variables, regression and correlation. The need for design, experimental design and sampling design. Sampling distributions, bias, variability. Probability models, random variables, probability laws. Prerequisite: Ontario Grade 12 Advanced Mathematics. Degree credit exclusions: AS/SC/MATH1131.03, SC/BIOL3080.03, SC/BIOL3090.03, AS/ECON2500.03, AS/SC/GEOG2420.03, AS/SC/PHED2050.03, AS/SC/PSYC2020.06, AS/SC/PSYC2021.03, AS/SOCI3030.06. Not open to any student who has successfully completed AS/SC/MATH2030.06. AS/SC/AK/MATH2570.03 Elementary Statistics II. Binomial distribution, sampling distribution of sample proportions and means, central limit theorem. Confidence intervals, tests and decisions, abuse of tests. Inference for a single mean, comparing two means, and for spread. Contingency tables. Simple regression and basic analysis of variance. Prerequisite: AS/SC/AK/MATH2560.03. Degree credit exclusions: AS/SC/MATH1132.03, SC/BIOL3080.03, SC/BIOL3090.03, AS/ECON3210.03, AS/ECON3500.03, AS/SC/GEOG2420.03, AS/SC/PSYC2020.06, AS/SC/PSYC2022.03, AS/SOCI3030.06. Not open to any student who has successfully completed AS/SC/MATH2030.06. AS/AK/MATH2580.06 Mathematics of Investment and Actuarial Science. Theory of interest; annuities certain; amortization and sinking funds; evaluation of bonds and other investments; depreciation, depletion and capital cost; insurance, including mortality tables, principles of life annuities, premiums and reserves. Prerequisite: One full university mathematics course. Degree credit exclusion: AS/SC/MATH2280.03. AS/SC/MATH3000.06 Problem Seminar. Heuristics (e.g., symmetry, subcases, parity, reformulation, recursion); pigeon hole principle; modular arithmetic; algebraic identities; summation of series; analytic methods; inequalities; vector and complex geometry. Prerequisites: One of AS/SC/AK/MATH1090.03, AS/SC/MATH1120.03, AS/SC/MATH2090.03, AS/SC/MATH2320.03; AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03; AS/SC/MATH2010.03 or AS/SC/MATH2015.03 or AS/SC/AK/MATH2310.03. AS/SC/AK/MATH3010.03 Vector Integral Calculus. Integrability of continuous functions over suitable domains, iterated integrals and Fubini's theorem, counterexamples, change of variables, Jacobian determinants, polar and spherical coordinates, volumes, vector fields, divergence, curl, line and surface integrals, Green's and Stokes' theorems, differential forms, general Stokes' theorem. Prerequisite: AS/SC/MATH2010.03, or AS/SC/AK/MATH2310.03, or AS/SC/MATH2015.03 and written permission of the Mathematics Undergraduate Director (normally granted only to students proceeding in Honours programmes in Mathematics or in the Specialized Honours Programme in Statistics). Prerequisite or corequisite: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03. Degree credit exclusion: AS/SC/MATH3310.03. AS/SC/AK/MATH3020.06 Algebra I. Introduction to the basic concepts of abstract algebra, with applications: groups (cyclic, symmetric, Lagrange's theorem, quotients, homomorphism theorems); rings (congruences, quotients, polynomials, integral domains, principal-ideal and unique-factorization domains); fields (field extensions, constructions with ruler and compasses, coding theory). Prerequisite: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03. AS/SC/AK/MATH3030.03 Stochastic Processes I. Discrete parameter stochastic processes, including sums of independent random variables: limit theorems (weak law of large numbers, central limit theorem), Markov chains, recurrence and transience, birth and death processes, branching processes. Prerequisite: AS/SC/AK/MATH2030.03. Degree credit exclusion: Not open to students who have completed or are taking AS/SC/MATH4430.03. AS/SC/MATH3033.03 Classical Regression Analysis. General linear model. Properties and geometry of least-squares estimation. General linear hypothesis, confidence regions and intervals. Multicollinearity. Relationship between ANOVA models and linear models. Residual analysis, outliers, partial and added variable plots. Prerequisite: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03. Corequisite: AS/SC/AK/MATH3131.03 or permission of the course coordinator. Degree credit exclusions: AS/SC/AK/MATH3330.03, AS/SC/GEOG3421.03, AS/SC/PSYC3030.06. AS/SC/MATH3034.03 Modern Regression Analysis. Selecting best model, cross-validation. Influence diagnostics. Weighted least squares, correlated errors, transformations, Box-Cox transformations. Logistic and Poisson regression. Generalized linear models. Multicollinearity, ridge regression. Topics selected from non-linear regression, scatterplot smoothing, non- parametric regression, additive non-linear regression, projection pursuit, robust regression. Prerequisite: AS/SC/MATH3033.03. Degree credit exclusions: AS/SC/AK/MATH3230.03, AS/SC/GEOG3421.03, AS/SC/PSYC3030.06. AS/SC/AK/MATH3050.06 Introduction to Geometries. Analytic geometry over a field with vector and barycentric coordinate methods, affine and projective transformations, inversive geometry, foundations of Euclidean and non-Euclidean geometry, applications throughout to Euclidean geometry. Prerequisite: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03 or permission of the course coordinator. AS/SC/MATH3100.03 Famous Problems in Mathematics. An attempt to foster an appreciation of the history, the personalities and some of the content of different areas of mathematics, by means of a study of some specific problems which have exercised the minds of mathematicians. Prerequisites: At least 12 credits from 2000-level MATH courses (without second digit 5) or permission of the course coordinator. AS/SC/AK/MATH3110.03 Introduction to Mathematical Analysis. Proofs in calculus and analysis. Topics include sets, functions, axioms for R, applications of the completeness axiom, countability, sequences and their limits, monotone sequences, limits of functions, continuity. Prerequisite: AS/SC/MATH1310.03 or AS/SC/MATH1014.03. Prerequisites or corequisites: AS/SC/AK/MATH2310.03 or AS/SC/MATH2010.03 or AS/SC/MATH2015.03; AS/SC/MATH2021.03 or AS/SC/AK/MATH2221.03 or AS/SC/MATH1025.03. Degree credit exclusion: AS/SC/MATH1010.03. AS/SC/AK/MATH3131.03 Mathematical Statistics I (formerly AS/SC/MATH3030.03 - before 1993/94). Topics include common density functions, probability functions, principle of likelihood, the likelihood function, the method of maximum likelihood, likelihood regions, tests of hypotheses, likelihood ratio tests, goodness of fit tests, conditional tests, and confidence sets with a view towards applications. Prerequisite: AS/SC/AK/MATH2030.03 or permission of the course coordinator. Degree credit exclusion: AS/SC/MATH3030.03 (taken before 1993/94). AS/SC/AK/MATH3132.03 Mathematical Statistics II (formerly AS/SC/MATH3031.03 - before 1993/94). Important examples and methods of statistical estimation and hypothesis testing are discussed in terms of their mathematical and statistical properties. Topics include sufficiency, Bayesian statistics, decision theory, most powerful tests, likelihood ratio tests. Prerequisite: AS/SC/MATH3030.03 (taken before 1993/94) or AS/SC/AK/MATH3131.03. Degree credit exclusions: AS/SC/MATH3031.03, AS/SC/MATH3130.03. AS/SC/MATH3140.06 Number Theory and Theory of Equations. A study of topics in number theory and theory of equations using relevant methods and concepts from modern algebra, such as Abelian groups, unique factorization domains and field extensions. Prerequisite: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03 or permission of the course coordinator. AS/SC/AK/MATH3170.06 Operations Research I. A study of linear programming; transportation problems, including network flows, assignment problems and critical path analysis; integer programming; dynamic programming and an introduction to stochastic models. Application to a set of problems representative of the field of operations research. Prerequisites: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03; SC/AS/COSC1530.03 or SC/AS/COSC1540.03 or equivalent. AS/SC/MATH3190.03 Set Theory and Foundations of Mathematics. The following topics are covered: paradoxes in native set theory; functions and relations, transfinite numbers, their ordering and their arithmetic; well-ordered sets and ordinal numbers; Zorn's lemma; an introduction to axiomatic set theory. Prerequisite(s): AS/SC/MATH2022.03, or AS/SC/AK/MATH2222.03, or both AS/SC/MATH2090.03 and AS/SC/MATH2320.03. AS/SC/AK/MATH3210.03 Principles of Mathematical Analysis. Rigorous presentation, with proofs, of fundamental concepts of analysis: limits, continuity, differentiation, integration, fundamental theorem. Prerequisite: AS/SC/MATH2010.03 or AS/SC/AK/MATH3110.03. AS/SC/AK/MATH3230.03 Analysis of Variance. Categorical variables; one factor and two factor analysis; fixed, random and mixed models; nested designs; an introduction to randomized block and Latin square designs. Second term. Prerequisite: AS/SC/AK/MATH3330.03. Degree credit exclusions: AS/SC/MATH3034.03, AS/SC/GEOG3421.03, AS/SC/PSYC3030.06. AS/SC/MATH3241.03 Numerical Methods I. An introductory course in computational linear algebra. Topics include simple error analysis, linear systems of equations, linear least squares and interpolation. (Same as SC/AS/COSC3121.03.) Prerequisites: SC/AS/COSC1030.03 or SC/AS/COSC1530.03 or SC/AS/COSC1540.03; AS/SC/MATH1025.03 or AS/SC/AK/MATH2221.03 or AS/SC/MATH2021.03. Degree credit exclusion: SC/AS/COSC3121.03. AS/SC/MATH3242.03 Numerical Methods II. Algorithms and computer methods for solving problems of differentiation, integration, differential equations, non-linear equations and unconstrained optimization. (Same as SC/AS/COSC3122.03.) Prerequisites: AS/SC/AK/MATH2270.03; AS/SC/MATH3241.03 or SC/AS/COSC3121.03. Degree credit exclusion: SC/AS/COSC3122.03. AS/SC/AK/MATH3260.03 Introduction to Graph Theory. Introductory graph theory with applications. Graphs, digraphs. Eulerian and Hamiltonian graphs. The travelling salesman. Path algorithms; connectivity; trees; planarity; colourings; scheduling; minimal cost networks. Tree searchs and sortings, minimal connectors and applications from physical and biological sciences. Prerequisite: At least 6 credits from 2000-level MATH courses (without second digit 5). AS/SC/AK/MATH3270.03 Dynamical Systems. Properties of vector fields and flows. Equilibrium and periodic solutions. Stability and energy function method. Invariant manifolds, Poincare- Bendixson theorem. Hopf-bifurcation, chaotic behaviours. Applications to interacting populations, reaction kinetics and damped sinusoidally driven pendulum. Prerequisites: AS/SC/MATH2021.03 or AS/SC/AK/MATH2221.03 or AS/SC/MATH1025.03; AS/SC/AK/MATH2270.03. AS/SC/MATH3271.03 Partial Differential Equations. Partial differential equations of mathematical physics and their solutions in various coordinates, separation of variables in Cartesian coordinates, application of boundary conditions; Fourier series and eigenfunction expansions; generalized curvilinear coordinates; separation of variables in spherical and polar coordinates. Prerequisites: AS/SC/AK/MATH2270.03; one of AS/SC/MATH2010.03, AS/SC/MATH2015.03, AS/SC/AK/MATH2310.03; AS/SC/AK/MATH3010.03 is also desirable, though not essential, as prerequisite for students presenting AS/SC/MATH2010.03 or AS/SC/AK/MATH2310.03. Degree credit exclusion: AS/MATH4200A.06. AS/SC/MATH3272.03 Special Functions. The special functions of mathematical physics: Bessel functions, Legendre functions, Gamma function, Hermite functions, Laguerre functions, Chebyshev polynomials, hypergeometric and confluent hypergeometric functions; boundary value problems, heat flow, wave motion in Cartesian and polar coordinates; Laplace and Fourier transforms. Prerequisite: AS/SC/MATH3271.03 or permission of the course coordinator. Degree credit exclusion: AS/MATH4200A.06. AS/SC/MATH3280.06 Actuarial Mathematics. Actuarial mathematics at a level appropriate for examination 150 of the Society of Actuaries. Topics include survival distributions and life tables, premiums and reserves for life insurance and annuities, multiple life functions, multiple decrement models, valuation theory of pension plans. Prerequisite: AS/SC/MATH2280.03. Prerequisite or corequisite: AS/SC/AK/MATH2030.03, or AS/SC/MATH3030.03 (taken before 1993/94). AS/SC/AK/MATH3330.03 Regression Analysis. Simple regression analysis, multiple regression analysis, matrix form of the multiple regression model, estimation, tests (t- and F-tests), multicollinearity and other problems encountered in regression, diagnostics, model building and variable selection, remedies for violations of regression assumptions. First term. Prerequisites: One of AS/SC/MATH1132.03, AS/SC/MATH2030.06, AS/SC/AK/MATH2570.03, AS/SC/PSYC2020.06, or equivalent; some acquaintance with matrix algebra (such as is provided in AS/SC/MATH1025.03, SC/MATH1505.06, AS/MATH1550.06, AS/SC/MATH2021.03, or AS/SC/AK/MATH2221.03). Degree credit exclusions: AS/SC/MATH3033.03, AS/ECON4210.03, AS/SC/GEOG3421.03, AS/SC/PSYC3030.06. AS/SC/AK/MATH3410.03 Complex Variables. An introduction to the theory of functions of a complex variable with applications to the evaluation of definite integrals, solution of two-dimensional potential problems, conformal mapping and analytic continuation. Prerequisite: AS/SC/MATH2015.03 or AS/SC/AK/MATH3010.03 or permission of the course coordinator. AS/SC/MATH3430.03 Sample Survey Design. Principal steps in planning and conducting a sample survey. Sampling techniques including simple random sampling, stratified random sampling, cluster sampling, and sampling with probabilities proportional to size. Estimation techniques including difference, ratio, and regression estimation. Prerequisite: AS/SC/AK/MATH2030.03, or AS/SC/MATH3030.03 (taken before 1993/94), or AS/SC/AK/MATH3330.03. AS/SC/MATH3440.03 The Mathematics of Physics. Various topics in physics which require mathematical analysis are discussed. The emphasis is on showing how such mathematical techniques as multivariable calculus, ordinary and partial differential equations, probability and calculus of variations arise in the study of these topics. Normally offered in alternate years. Prerequisite: AS/SC/AK/MATH2270.03. Prerequisite or corequisite: AS/SC/MATH2015.03 or AS/SC/AK/MATH3010.03. Degree credit exclusion: Not open to Physics majors. AS/SC/MATH3450.03 Introduction to Differential Geometry. Curves and surfaces in 3-space, tangent vectors, normal vectors, curvature, introduction to topology and to manifolds. Prerequisites: AS/SC/AK/MATH3010.03; AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03; or permission of the course coordinator. Degree credit exclusion: AS/SC/AK/MATH4250.06. AS/SC/MATH3480.03 Introductory Topology. Elementary concepts of the topology of the plane. Neighbourhoods, continuity, open and closed sets, compactness, connectedness. Fixed point theorems. Homotopies of curves. Combinatorial classification of surfaces. Some three-dimensional topology. Metric spaces. Prerequisite: AS/SC/MATH2010.03 or AS/SC/MATH2015.03 or AS/SC/AK/MATH2310.03 or permission of the course coordinator. AS/MATH3500.06 Mathematics in the History of Culture. An introduction to the history of mathematical ideas from antiquity to the present, with emphasis on the role of these ideas in other areas of culture such as philosophy, science and the arts. (Same as AS/HUMA3990A.06.) Prerequisite: 6 credits in university-level mathematics (other than AS/SC/MATH1500.03, AS/SC/MATH1510.06, AS/MATH1520.06, AS/SC/MATH1525.03, or SC/ACMS1530.06) is strongly recommended. Degree credit exclusion: AS/HUMA3990A.06. AS/SC/MATH4000.06 (4000.03) Individual Project. A project of a pure or applied nature in mathematics or statistics under the supervision of a faculty member. The project allows the student to apply mathematical or statistical knowledge to problems of current interest. A report is required at the conclusion of the project. Prerequisites: Open to students in Honours programmes in Applied Mathematics, Mathematics, and Statistics. Permission of the course coordinator is required. AS/SC/AK/MATH4010.06 Real Analysis. Survey of the real and complex number systems, and inequalities. Metric space topology. The Riemann-Stieltjes integral. Some topics of advanced calculus, including more advanced theory of series and interchange of limit processes. Lebesgue measure and integration. Fourier series and Fourier integrals. Prerequisite: AS/SC/AK/MATH3210.03 or permission of the course coordinator. AS/SC/AK/MATH4020.06 Algebra II. Continuation of Algebra I, with applications: groups (finitely generated Abelian groups, solvable groups, simplicity of alternating groups, group actions, Sylow's theorems, generators and relations); fields (splitting fields, finite fields, Galois theory, solvability of equations); additional topics (lattices, Boolean algebras, modules). Prerequisite: AS/SC/AK/MATH3020.06 or permission of the course coordinator. AS/SC/AK/MATH4030.03 Probability Theory. Elementary measure theory, convergence of random variables, strong law of large numbers, convergence in distribution, stable laws, conditional expectation, martingales. Prerequisite: AS/SC/MATH3030.03 (taken after 1993/94) or AK/MATH3030.03. AS/SC/AK/MATH4080.06 Topology. Topological spaces, continuity, connectedness, compactness, nets, filters, metrization theorems, complete metric spaces, function spaces, fundamental group, covering spaces. Prerequisite: AS/SC/MATH3480.03 or AS/SC/AK/MATH3210.03 or permission of the course coordinator. AS/SC/MATH4100.03 Topics in Mathematical Education. This course consists of a series of presentations, by the students, of mathematical topics chosen in consultation with the instructor. Suitability of the material for presentation in high schools is discussed. Prerequisite: Permission of the course coordinator. for 1995/96 AS/SC/MATH4100A.03 Topics in Mathematical Education: Theory and Practice. ... (condensed course description of approximately 40 words) ... A two-hour seminar every two weeks, practical hours. Two terms. Three credits. Prerequisites: All 1000- and 2000-level core requirements for an Honours degree programme in Applied Mathematics, Mathematics, Mathematics for Commerce, or Statistics; permission of the course coordinator. Note: This course is open to students enrolled in the Intermediate/Senior concurrent Education programme, but may not be used to satisfy any of the requirements for a first or second teaching subject. AS/SC/MATH4110.03 Topics in Analysis. One or two topics which may be chosen from the following: special functions, integral transforms, Fourier series, divergent series, asymptotic expansions, theory of approximation, partial differential equations, calculus of variations, calculus of manifolds, introduction to functional analysis, difference equations. Prerequisite: Permission of the course coordinator. AS/SC/MATH4120.03 Topics in Algebra. One or two topics which may be chosen from the following: category theory, commutative algebra, infinite Abelian groups, non-associative algebras, presentation theory, representations of finite groups, universal algebra. Prerequisite: Permission of the course coordinator. AS/SC/MATH4130.03 Topics in Probability and Statistics. One or two topics which may be chosen from the following: statistical decision theory, statistical inference, sequential analysis, information theory, large sample theory, design of experiments, stochastic processes, time series. Prerequisite: Permission of the course coordinator. AS/SC/MATH4140.03 Topics in Number Theory. Topics chosen from quadratic diophantine equations and infinite continued fractions, elements of algebraic number theory, p-adic numbers, other topics selected according to student interest. Prerequisite: Permission of the course coordinator. AS/SC/MATH4141.03 Advanced Numerical Methods. Systems of non- linear equations: Newton-Raphson, quasi Newton methods; optimization problems: steepest descents, conjugate gradient methods; approximation theory: least squares, singular value decomposition, orthogonal polynomials, Chebyshev and Fourier approximation, Pade approximation; matrix eigenvalues: power method, householder, QL and QR algorithms. Prerequisite: AS/SC/MATH3242.03 or SC/AS/COSC3122.03. AS/SC/MATH4142.03 Numerical Solutions to Partial Differential Equations. Review of partial differential equations, elements of variational calculus; finite difference methods for elliptic problems, error analysis, boundary conditions, non-Cartesian variables, PDE-eigenvalue problems; hyperbolic and parabolic problems, explicit and implicit methods, stability analysis; Rayleigh-Ritz and Galerkin method for ODEs, finite element methods. Prerequisites: AS/SC/AK/MATH2270.03; AS/SC/MATH3242.03 or SC/AS/COSC3122.03; AS/SC/MATH3272.03 is strongly recommended. AS/SC/MATH4150.03 Topics in Geometry. One or two topics which may be chosen from the following: projective geometry, algebraic geometry, geometrical algebra, finite geometries, differential geometry, Riemannian geometry, discrete applied geometry. Prerequisites: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03; 6 credits from 3000-level MATH courses (without second digit 5); or permission of the course coordinator. for 1995/96 AS/SC/MATH4150C.03 Topics in Geometry: Geometries from a Transformation Point of View. ... (condensed course description of approximately 40 words) ... Prerequisites: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03; 6 credits from 3000-level MATH courses (without second digit 5); or permission of the course coordinator. AS/SC/MATH4160.03 Combinatorial Mathematics. Topics from algebra of sets, permutations, combinations, occupancy problems, partitions of integers, generating functions, combinatorial identities, recurrence relations, inclusion-exclusion principle, Polya's theory of counting, permanents, systems of distinct representatives, Latin rectangles, block designs, finite projective planes, Steiner triple systems. Prerequisites: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03; 6 credits from 3000-level MATH courses (without second digit 5); or permission of the course coordinator. AS/SC/MATH4170.06 Operations Research II. Selected topics from game theory, decision theory, simulation, reliability theory, queuing theory, non-linear programming, classification, pattern-recognition and prediction. Each chapter contains an optimization problem and methods and algorithms for solving it. The course is rich in examples. Prerequisites: AS/SC/MATH2010.03 or AS/SC/MATH2015.03 or AS/SC/AK/MATH2310.03; AS/SC/MATH1132.03 or AS/SC/MATH2030.06 or AS/SC/AK/MATH2030.03; AS/SC/AK/MATH3170.06; or permission of the course coordinator. Degree credit exclusion: AS/MATH4570.06. AS/SC/MATH4200.06 (4200.03) Special Topics. The department may offer courses or seminars on particular topics not ordinarily available. Some Special Topics courses may not be eligible for Science (SC) credit. Two terms. Six credits. One term. Three credits. Prerequisite: Permission of the course coordinator. AS/SC/AK/MATH4210.03 Complex Analysis. Development of the principal results in complex variable theory, including Taylor and Laurent series, the calculus of residues, the maximum modulus theorem and some special functions. Introduction to some more advanced topics. Prerequisite: AS/SC/AK/MATH3410.03 or permission of the course coordinator. AS/SC/MATH4230.03 Non-Parametric Methods in Statistics. Order statistics; general rank statistics; one-sample, two-sample, and k-sample problems; Kolmogorov-Smirnov statistics; tests of independence and relative efficiencies. Prerequisite: AS/SC/MATH3030.03 (taken before 1993/94) or AS/SC/AK/MATH3131.03; AS/SC/MATH3031.03 or AS/SC/AK/MATH3132.03 is recommended but not required. AS/SC/MATH4240.03 Topics in Applied Mathematics. One or two topics which may be chosen from the following: A numerical analysis B discrete applied mathematics C operations research D mathematical physics E mathematical biology G mathematical modelling Normally offered in alternate years. Prerequisite: Permission of the course coordinator. AS/SC/MATH4241.03 Applied Group Theory (formerly AS/SC/MATH4120M.03 - before 1995/96). Introduction to group theory and its applications in the physical sciences. Finite groups. Compact Lie groups. Representation theory, tensor representations of classical Lie groups, classification of semi- simple Lie groups. Prerequisite: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03. Degree credit exclusion: AS/SC/MATH4120M.03. AS/SC/AK/MATH4250.06 Differential Geometry. Curves and surfaces in 3-space, tangent vectors, normal vectors, curvature, introduction to topology, manifolds, tangent spaces, multilinear algebra and tensors. Normally offered in alternate years. Prerequisites: AS/SC/AK/MATH3010.03; AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03; or permission of the course coordinator. Degree credit exclusion: AS/SC/MATH3450.03. AS/SC/MATH4270.03 Integral Transforms and Equations. This course studies the Laplace, Fourier, Hankel and Mellin transforms; the solution of integral equations; and the treatment of asymptotic expansions. The applications are to problems in circuit theory, heat flow, elasticity, transport theory and scattering theory. Prerequisites: AS/SC/AK/MATH2270.03; AS/SC/AK/MATH3410.03. Prerequisite(s) or corequisite: AS/SC/MATH3271.03; AS/SC/MATH3272.03. AS/SC/MATH4280.03 Risk Theory. A study of the stochastic aspects of risk with emphasis on insurance applications. Topics include an introduction to utility theory, individual and collective risk theory, compound Poisson processes, ruin theory, non-proportional reinsurance. Prerequisite: AS/SC/AK/MATH2030.03, or AS/SC/MATH3030.03 (taken before 1993/94); AS/SC/MATH3280.06 is recommended but not required. AS/SC/MATH4290.03 Mathematical Logic. Predicate logic, rules of inference, elimination of quantifiers, semantics and model theory, the completeness and compactness theorems, ultrapowers and non-standard analysis. Prerequisite: AS/SC/MATH2090.03 or permission of the course coordinator. AS/SC/MATH4300.06 (4300.03) Directed Readings. A student may arrange to do independent study with a member of the Mathematics and Statistics Department. Such an arrangement must have prior approval of the department Chair. Faculty of Arts students should see page ## for regulations governing independent reading courses. Some Directed Readings topics may not be eligible for Science (SC) credit. Two terms. Six credits. One term. Three credits. AS/SC/MATH4400.06 The History of Mathematics. Selected topics in the history of mathematics, discussed in full technical detail but with stress on the underlying ideas, their evolution and their context. Prerequisites: 36 credits from MATH courses (without second digit 5), including at least 12 credits at or above the 3000 level. (12 of the 36 credits may be taken as corequisites.) AS/SC/MATH4430.03 Stochastic Processes II. Continuous parameter stochastic processes: Markov jump processes, Poisson processes, renewal theory. Topics from queuing theory, Brownian motion, stationary processes. Prerequisite: AS/SC/MATH3030.03 (taken after 1993/94) or AK/MATH3030.03. AS/SC/MATH4470.03 Gas and Fluid Dynamics. Fundamental laws; conservation of mass, momentum and energy; vortex motion; incompressible, compressible and viscous flows; turbulent flow; surface waves. (Same as SC/PHYS4120.03.) Prerequisites: AS/SC/MATH2015.03; AS/SC/AK/MATH2270.03; SC/PHYS2010.03 or SC/EATS2470.04. Degree credit exclusions: SC/PHYS3180.03, SC/PHYS4120.03. AS/MATH4501.03 Financial Accounting. This introduction to financial accounting takes a conceptual approach with heavy emphasis on concepts and on case analysis. It examines the concepts, principles, and practices of financial accounting from the perspective of the users of financial statements. (Same as AS/CC4501.03.) Degree credit exclusions: AS/CC4501.03, AS/ECON3580.03, AD/ACTG2010.03, AD/ACTG2011.03, AD/ACTG3000.03, AD/ACTG5010.03, AD/ACTG5100.03. AS/MATH4502.03 Managerial Accounting. This course focuses on the basic accounting concepts that form the foundation for management decisions. Performance appraisal, pricing, financing, output, investment, and other similar managerial decisions are examined and applied in case situations. Technical aspects of management accounting are not emphasized. (Same as AS/CC4502.03.) Prerequisite: AS/MATH4501.03 or AS/CC4501.03. Degree credit exclusions: AS/CC4502.03, AS/ECON3590.03, AD/ACTG3020.03, AD/ACTG5020.03, AD/ACTG5210.015. AS/MATH4570.06 Applied Optimization. Topics chosen from decision theory, game theory, inventory control, Markov chains, dynamic programming, queuing theory, reliability theory, simulation, non- linear programming. This course is designed primarily for students in the General Stream of Honours Mathematics for Commerce. Prerequisites: AS/SC/AK/MATH3170.06; AS/SC/AK/MATH3330.03; AS/SC/AK/MATH3230.03 or AS/SC/MATH3430.03. Degree credit exclusion: AS/SC/MATH4170.06. AS/SC/MATH4630.03 Applied Multivariate Statistical Analysis. The course covers the basic theory of the multivariate normal distribution and its application to multivariate inference about a single mean, comparison of several means and multivariate linear regression. As time and interest permit, further related topics may also be covered. Prerequisites: AS/SC/MATH3030.03 (taken before 1993/94) or AS/SC/AK/MATH3131.03; AS/SC/MATH3034.03 or AS/SC/AK/MATH3230.03; AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03. AS/SC/MATH4730.03 Experimental Design. An examination of the statistical issues involved in ensuring that an experiment yields relevant information. Topics include randomized block, factorial, fractional factorial, nested, Latin square and related designs. Further topics as time permits. The emphasis is on applications. Prerequisites: A second 6 credits in statistics; including either AS/SC/MATH3033.03, or both AS/SC/AK/MATH3230.03 and AS/SC/AK/MATH3330.03, or permission of the course coordinator. AS/SC/MATH4830.03 Time Series and Spectral Analysis. Treatment of discrete sampled data by linear optimum Wiener filtering, minimum error energy deconvolution, autocorrelation and spectral density estimation, discrete Fourier transforms and frequency domain filtering and the Fast Fourier Transform algorithm. (Same as SC/EATS4020.03 and SC/PHYS4060.03.) Prerequisites: SC/AS/COSC1540.03 or equivalent FORTRAN programming experience; AS/SC/AK/MATH2270.03; one of AS/SC/MATH2010.03 (before FW92), AS/SC/MATH2015.03, AS/SC/MATH2310.03 (before FW92), AS/SC/AK/MATH3010.03. Degree credit exclusions: SC/AS/COSC4010B.03, SC/AS/COSC4242.03, SC/EATS4020.03, SC/PHYS4060.03. AS/SC/MATH4930.03 Topics in Applied Statistics. Each time this course is given, it is on a topic chosen from the following: A statistical quality control B simulation and the Monte Carlo method C forecasting and applied time series D applied decision theory. Prerequisites: AS/SC/AK/MATH3330.03; AS/SC/AK/MATH3230.03 or AS/SC/MATH3430.03. Corerequisite (for AS/MATH4930A.03 only): AS/SC/MATH4730.03. Degree credit exclusion (for AS/MATH4930B.03 only): SC/AS/COSC3408.03. for 1995/96 AS/SC/MATH4930B.03 Topics in Applied Statistics: Simulation - a Statistical Perspective. ... (condensed course description of approximately 40 words) ... Prerequisites: AS/SC/AK/MATH3330.03; AS/SC/AK/MATH3230.03 or AS/SC/MATH3430.03. Degree credit exclusion: SC/AS/COSC3408.03. ... STATISTICS - ARTS, PURE AND APPLIED SCIENCE See Mathematics and Statistics.