Department of Mathematics: 1000 Level Courses Faculty of Science

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1 Department of Mathematics: 1000 Level Courses information for prospective students published by the Dean s Office, Introduction The Department of Mathematics offers a wide variety of 1000 level courses that a student may wish to take in Year 1. These courses are designed to meet a variety of needs: to help meet the requirement that all students take at least a half-course with substantial university level mathematics content; to meet the developmental requirements of students with weak backgrounds in mathematics; and to provide service to the diverse groups of students who require half-courses in calculus or linear algebra, whether in preparation for entry into a professional program or in preparation for academic programs requiring mathematics. A listing of these 1000 level courses follows. These courses are listed under the Department of Mathematics in the University of Manitoba Undergraduate Calendar. An abridged copy of the calendar listings is found in this infosheet; this includes prerequisites, which are not the same for all courses. Because there are so many 1000 level courses, choosing the right course(s) for your needs may seem difficult. This document will provide guidance to you as you make your choices. You can obtain help by phoning (204) or by mathematics_dept@umanitoba.ca. Prerequisites: A grade of 60% or better in Precalculus 40S is the pre-requisite for entry into all 1000 level courses numbered MATH 1200 and above (with minor exceptions for MATH 1300 and MATH 1310; see the section below and the detailed Course Descriptions beginning on page 5). See Chart 1 on page 3 for more information. Note that Applied Mathematics 40S cannot be substituted for Precalculus 40S for this purpose, except in two very special situations described below. What to do if you lack the prerequisites Some students need to take introductory calculus, and perhaps MATH 1300 or MATH 1310, to be eligible to enter certain faculties or programs. A student in this position, but lacking a grade of 60% or better in Mathematics (Precalculus) 40S, can proceed as follows. Register in "Mathematical Skills" (see below) in Fall Term and earn a "C" or better. Then register in calculus (and one of MATH 1300 and MATH 1310 if your program requires it) in Winter Term. The courses MATH 1500 and MATH 1300 will also be taught in May and June, so another possibility would be to take one of them in Winter Term and the other in May and June. The two "special situations" in which Applied Mathematics 40S can be used as a prerequisite are these: a student with a grade of 70% or better in Applied Mathematics 40S can use this (instead of Mathematics (Precalculus) 40S) as a prerequisite for either MATH 1300 or MATH Such students could (if they need to) take MATH 1300 or MATH 1310, together with the "Mathematical Skills" course, in Fall Term, and then (assuming they receive a grade of "C" or better in Mathematical Skills) take an introductory calculus course (MATH 1500 or MATH 1520) in Winter Term. The Mathematical Skills Course The Extended Education Division at the University of Manitoba offers the non-credit course, Mathematical Skills. This course is designed for, but not exclusive to, students preparing to enter first year mathematics courses at the University of Manitoba. For registration information call Student Services at (or Manitoba toll free at: extension 8016). Department of Mathematics Page 1

2 Choosing courses Students deciding which mathematics courses to take at University should consider two factors: their aptitude for mathematics and how well they know their high school mathematics One's grade in the high school course Mathematics PreCalculus 40S (or its equivalent from outside Manitoba) will be a good indication of that. Chart I on page 3 provides advice on course selection based on this factor. the program of studies they plan to follow Chart II on page 4 provides advice based on this factor. Students should consult the University's annual Undergraduate Calendar for more detailed advice concerning their planned programs of study. MATH 0500 The Department of Mathematics has developed two new programs available, on a voluntary basis, to all students registered in Mathematics courses 1200, 1210, 1300, 1310, 1500, 1510, 1520, 1700, and The diagnostic test is a voluntary on-line 50- question test, whose purpose is to measure your potential for success in the above Mathematics courses. The questions test your knowledge and skill in topics contained in the high school mathematics curriculum, principally Pre-Calculus 40S. The test provides you with an assessment of your knowledge and skill level, and provides advice about actions you should take in order to increase your chances of success in mathematics courses. Access to the Mathematics Diagnostic Test is gained from your personal WebCT Homepage. If your results on the diagnostic test indicate that you would benefit by improving your mathematical skills, you should purchase a copy of the notes prepared for this purpose, entitled Preparing for University Mathematics. Enroll in one of sections of the noncredit course MATH 0500 Preparing for University Mathematics. This course will be offered on Saturday mornings (9:00 am until noon) during the first half of the school term. Enrollment in each section will be limited to 25 students. During these sessions a graduate student from the Department of Mathematics will serve as a tutor. Courses included in the program A three credit course, also called a half course, runs over one term. A six credit course or full course spans two terms. The courses marked with an * are also available en français at Collège universitaire de Saint- Boniface. (Credit hours are indicated in parenthesis.) MATH 1010 Applied Finite Mathematics (3) MATH 1020 Mathematics and Art (3) MATH 1190 Topics in Mathematics (6) MATH 1200 Elements of Discrete Mathematics* (3) MATH 1210 Techniques of Classical & Linear Algebra (3) MATH 1300 Vector Geometry & Linear Algebra* (3) MATH 1310 Matrices for Management & Social Sciences (3) MATH 1500 Introduction to Calculus* (3) MATH 1510 Applied Calculus I (3) MATH 1520 Introductory Calculus for Management & Social Sciences (3) Calculus II* (3) MATH 1710 Applied Calculus II (3) Notes on Courses MATH 1010, MATH 1020 and MATH 1190 The courses MATH 1010, Applied Finite Mathematics, MATH 1020, Mathematics in Art, and MATH 1190, Topics in Mathematics, are general interest courses. Students without a strong mathematics background, or without prerequisites for other mathematics courses, are encouraged to take either MATH 1010, MATH 1020 or MATH 1190 to fulfill the University requirements that all students must have 3 credit hours in a course with a substantial mathematical content. (MATH 1020 is taught with School of Art FA 1020 and has limited enrollment.) Students entering any program that uses mathematics are urged to select courses from those with course numbers MATH 1200 or higher. NOTE: Students holding credit in MATH 1200 or higher cannot take these three courses. Department of Mathematics Page 2

3 CHART I: Choosing University Mathematics courses based on Senior 4 courses Mathematics Pre-Calculus 40S mark in percentage (or equivalent) Best choice of University mathematics course No Pre-Calculus 40S or less than 60% You can take MATH 1010, MATH 1020 or MATH To take any other University mathematics course, take the Math Skills course from Continuing Education (a non-degree, non-credit course) or take/repeat Pre-calculus 40S through a school division or by correspondence. 60% - 69% You are eligible to take any of the first year mathematics courses, but are likely to experience some difficulties with many parts of these courses. You may benefit from taking the Mathematical Skills course from Continuing Education before attempting any course numbered MATH 1200 or above. Alternately, some of the introductory courses (MATH 1310, MATH 1500 and MATH 1520) have "developmental" sections, in which there are extra classes devoted to review. You should consider enrolling in a developmental section. 70% - 79% You are eligible to take any of the first year Mathematics courses but some concern about your basic mathematical skills may still be appropriate. You might choose to enroll in a "developmental" section (see above). 80% - 100% You are eligible to take any of the first year Mathematics courses. Assuming you have good study skills and work habits, you should succeed in any introductory course. Applied Mathematics 40S mark in percentage % You can take MATH 1010, MATH 1020, MATH 1190, MATH 1300 or MATH To take any other University mathematics course, take the Math Skills course from Continuing Education, or Pre-Calculus 40S through a school division or by correspondence. Department of Mathematics Page 3

4 CHART II: Choosing your mathematics course by your intended program of study ABBREVIATIONS: In what follows, "MATH 13A0" means either MATH 1300 or MATH 1310; "MATH 15A0" means one of MATH 1500, MATH 1510 or MATH 1520; and "MATH 17A0" means one of or MATH Intended program of study Faculty of Agricultural & Food Sciences Faculty of Arts Required courses for entry to program See Faculty of Agricultural and Food Sciences section of the Undergraduate Calendar 3 credit hours from list of approved mathematics courses (see Faculty of Arts section of the Undergraduate Calendar) Recommended courses (see Remark 1 on next page) MATH 1010 or MATH 1190 (see note following Chart I) Faculty of Arts (Honours Economics) 6 credit hours from MATH 13A0, MATH 15A0 or MATH 17A0 (see Remark 3 on next page) MATH 1300 and MATH 1500 Faculty of Engineering MATH 1210, MATH 1510 and MATH 1710 MATH 1210, MATH 1510 and MATH 1710 Clayton H. Riddell Faculty of Environment, Earth and Resources (Geophysics Honours) MATH 1210, MATH 15A0 and MATH 17A0, MATH 1210, MATH 1500 and Faculty of Management (non Actuarial pattern) Faculty of Management (Actuarial pattern) MATH 15A0 (see Remarks 3 and 4 on next page) MATH 15A0 MATH 1520 Faculty of Pharmacy MATH 15A0 MATH 1500 (Honours Biological Sciences) (Biochemistry, Chemistry) (Computer Science) (Mathematics major) (Physics) (Statistics major) MATH 15A0 and MATH 17A0 MATH 13A0 and MATH 15A0 (see Remark 3 on next page) MATH 13A0, MATH 15A0 and MATH 17A0 MATH 13A0, MATH 15A0, MATH 17A0 and MATH 1200 is required for the Major MATH 1200, MATH 13A0, MATH 15A0 and MATH 17A0 (see Remarks 3 and 4 on next page) MATH 1200, MATH 1300 or MATH 1500 (see Remark 1 on next page) MATH 1500 and MATH 1300 and MATH 1500 ; perhaps also MATH 1200 Fine Arts 3 credit hours MATH 1020 Department of Mathematics Page 4

5 Remarks 1. Recommendations are indicated where there is a choice among required courses or where it is advisable that a course be taken in first year. Students intending to enter a specific faculty and/or major program within that Faculty are urged to consult the University of Manitoba Undergraduate Calendar and/or representatives of the Faculty/program in question, for more information. 2. MATH 1500 and MATH 1510 are always interchangeable as prerequisites for later courses in Mathematics, as are and MATH Other departments and faculties may not provide similar flexibility in the use of our courses as prerequisites and corequisites for their courses and programs. You are advised to consult their prerequisite and corequisite requirements as described in the University of Manitoba Undergraduate Calendar. 3. Students planning to study Linear Algebra beyond Year I are advised to elect MATH Students who intend to take more than 3 credit hours of Year I calculus are advised to take MATH 1500, or MATH 1510, rather than MATH MATH 1510 has the high school course Physics 40S as a prerequisite. MATH 1710 has the University physics course PHYS 1050 as a corequisite. Examples drawn from physics will be used in these courses. 5. For details regarding Mathematics prerequisites for entry to the Honours and Major programs see the University Undergraduate Calendar. Course descriptions This is an abridged version of course descriptions of the 1000 level Mathematics courses found in the University of Manitoba Undergraduate Calendar. A complete list of all undergraduate mathematical sciences courses which are presently approved by Academic Senate is available in the University of Manitoba Undergraduate Calendar. NOTE: Unless otherwise specified, a minimum grade of C must be achieved for any course stipulated as prerequisite to a further course in Mathematics. MATH 1010 Applied Finite Mathematics (3)L For students needing to fill the requirement of a university level mathematics course. This course introduces students to modern applications of discrete mathematics. Topics include: mathematics of finance, linear programming, graph theory and game theory. This course cannot be used as part of an Honours, Major, General or Minor program in the Mathematical Sciences. MATH 1020 Mathematics in Art (3) For students needing to fill the requirement of a university level mathematics course. It introduces students to mathematical methods and principles in works of art in relation to Euclidean and non- Euclidean geometrics. Topics include: linear perspective; shapes, patterns and balance; proportion, ratio and harmony; symmetry, geometry, and the study of different surfaces. This course has limited enrollment. It may not be used as part of an Honours, Major, General or Minor program in the Mathematical Sciences. MATH 1190 Topics in Mathematics (6) This course is designed to give students in various faculties a measure of insight into modern mathematics. Topics are taken from number systems, geometry and combinatorics. This is a terminal course and may not be used as a prerequisite for other Mathematics courses. It may not be used as part of an Honours, Major, General or Minor program in the Mathematical Sciences. MATH 1200 Elements of Discrete Mathematics (3) Sequences and series, trigonometry, complex numbers, algebra of polynomials, approximation of zeros of functions, linear difference equations. Prerequisite: a minimum grade of 60% in Math Pre- Calculus 40S (300), or grade of C or better in the Mathematical Skills course taught by the Continuing Education Division. Not to be held with MATH Department of Mathematics Page 5

6 MATH 1210 Techniques of Classical & Linear Algebra(3)L An introduction to a variety of practical algebraic concepts and skills necessary for the study of calculus and advanced engineering mathematics. The emphasis of this course is in the development of methodology and algebraic skill necessary for successful completion of subsequent engineering mathematics courses. Applications in this course make it especially suitable for students intending to take programs in Engineering. Not to be held with MATH 1200, 1300, or MATH Prerequisite: a minimum grade of 60% in Math Pre-Calculus 40S (300) or a grade of C in the Mathematical Skills course taught by the Continuing Education Division. MATH 1300 Vector Geometry and Linear Algebra (3)L An introduction to vectors, matrices, systems of linear equations and three-dimensional geometry. Not to be held with MATH 1210 or MATH Prerequisite: a minimum grade of 60% in Math Pre- Calculus 40S (300), or a minimum grade of 70% in Applied Math 40S, or grade of C in he Mathematical Skills course taught by the Continuing Education Division. MATH 1310 Matrices for Management & Social Sciences (3)L Matrix methods with examples relevant to the Management and Social Sciences. Topics include vectors, matrices, systems of linear equations and determinants; applications include economic models, the simplex method for linear programming, Markov chains, and game theory. Not to be held with MATH 1210 or MATH Prerequisite: a minimum grade of 60% in Math Pre- Calculus 40S (300), or a minimum grade of 70% in Applied Math 40S, or a grade of C in the Mathematical Skills course taught by the Continuing Education Division. MATH 1500 Introduction to Calculus (3)L Differentiation and integration of elementary functions, with applications to maxima and minima, rates of change, area and volume. Not to be held with MATH 1510 or MATH Prerequisite: a minimum grade of 60% in Math Pre-Calculus 40S (300) or a grade of C in the Mathematical Skills course taught by the Continuing Education Division. MATH 1510 Applied Calculus (3)L Functions and graphs, limits and continuity, differentiation of functions defined explicitly and implicitly; applications of derivatives to velocity and acceleration, related rates, maxima and minima; differentials, indefinite and definite integrals. Physical applications in this course make it especially suitable for students intending to take programs in engineering. Not to be held with MATH 1500 or MATH Prerequisites: a minimum grade of 60% in Math Pre-Calculus 40S (300) or a grade of C in the Mathematical Skills course taught by the Continuing Education Division, Physics 40S (300) or a pass in PHYS MATH 1520 Introductory Calculus for Management and Social Sciences (3)L Differentiation and integration of functions of one variable and partial differentiation of functions of several variables. Emphasizes applications in the areas of management and social science. Not to be held with MATH 1500 or MATH Prerequisite: a minimum grade of 60% in Math Pre-Calculus 40S (300) or equivalent or a pass in the Mathematical Skills course taught by the Continuing Education Division. Calculus II (3)L Theory and techniques of integration, curve sketching, volume, arc length, surface area and partial derivatives. Not to be held with MATH Prerequisites: MATH 1500 or MATH Department of Mathematics Page 6

7 MATH 1710 Applied Calculus II (3)L Applications of integration to volumes, centres of mass, moments of inertia, work and fluid pressure; differentiation of trigonometric exponential and logarithmic functions; techniques of integration, polar co-ordinates. Physical applications in this course make it especially suitable for students intending to take programs in engineering. Not to be held with. Prerequisite: MATH 1500 or MATH Corequisite: PHYS For further information THE UNIVERSITY OF MANITOBA Please contact: Department of Mathematics 342 Machray Hall, The University of Manitoba Winnipeg MB R3T 2N2 Telephone: (204) FAX: (204) website: umanitoba.ca/science/mathematics/ Note: In the event of any inconsistencies between the information provided in this Infosheet and the University's annual Undergraduate Calendar, the Calendar entry shall prevail. The effective date of information provided in this Infosheet is September Department of Mathematics Page 7