Mathematics 225

Course Outline

LENGTH OF COURSE: One Semester (14 weeks)
 
CLASSROOM HOURS PER WEEK: 4 hours of lectures
 
NUMBER OF UNITS OF CREDIT: 3 credit hours
    Simon Fraser University - 3 credit hours
    University of British Columbia - 3 credit hours
    University of Victoria - 1.5 units
PRESENT TRANSFERABILITY
    Simon Fraser University - Mathematics 242 (3)
    University of British Columbia - Mathematics 220 (1.5)
    University of Victoria - Mathematics 200 level (1.5)
PREREQUISITE: Columbia College Mathematics 113 and 114 or the equivalent. (With permission of the instructor, students may take Mathematics 114 concurrently.)
 
AUDIENCE: This course is intended for students planning to major in mathematics or science.
 
CALENDAR DESCRIPTION
A theoretical course investigating some of the principles that underlie Mathematics 113 and 114. Mathematics 225 is designed for students anticipating a major in mathematics or science.
 
COURSE OUTLINE
1) Limits of Sequences and the Real Number System (4 weeks)
Sequences, iteration, properties of real numbers, limit of a sequence (informal notion as well as formal definition), completeness of the real numbers, definition of e and its properties, convergence and divergence of sequences, countability, Cantor's diagonal method.
 
2) Infinite Series (3 weeks)
Convergence and divergence of infinite series, harmonic series, convergence tests (comparison test, ratio test, root test), absolute vs. conditional convergence, power series.
 
3) Limits of Functions, Continuity, Differentiability (4 weeks)
Limit of a function (informal notion and formal definition), limits at infinity, one-sided limits, formal definition of continuity, continuity theorems, types of discontinuities, differentiability, differentials, proofs of differentiability theorems.
 
4) Properties of Continuous Functions (2 weeks)
Supremum and infimum, Bolzano-Weierstrass property, Cauchy sequences, intermediate value theorem, uniform continuity.
 
TEXTBOOK
    Colin Clark, Elementary Mathematical Analysis, Second Edition, Wadsworth 1982
    Sections of the textbook relevant to the above topics: 1) Chapter 1 2) Chapter 2 3) Chapter 3 4) Chapter 4
COURSE EVALUATION
    Quizzes and/or Assignments 10%
    Three One-Hour Tests 40%
    Comprehensive Final Exam 50%
INSTRUCTORS
    Kim Peu Chew, B.Sc. (Nanyang), M.A., Ph.D. (British Columbia)
    Sam Ekambaram, B.Sc. (Madras), Ph.D. (Simon Fraser)
    Peter Hurthig, B.Sc., M.Sc. (Briitsh Columbia)
    David Medalen, B.A. (St.Olaf), M.Sc. (British Columbia)