MAT 157 University of Toronto 2023-24

MAT 157Y1Y Analysis I, 2023-24

Almut Burchard, Instructor

SCHEDULE

Lectures MWF 10:10-11am, ES 1050

8 tutorial sections (Fall; M 4-6pm, T 9-11am, W 2-4pm, R 9-11am)

4 practical sections (Winter; M 4-6pm, T 9-11am, W 2-4pm, R 9-11am)

How to reach me: Almut Burchard, Bahen Center Rm. 6234, 8-3318.

www.math.utoronto.ca/almut/

You can email me through Quercus, or directly to almut @math.toronto.edu

I am available for questions after lectures in front of the lecture hall
Office hour: Wednesdays 12-1pm

Teaching assistants: Alejandro Adames (alejandro.adames), Antun Dvorski (a.dvorski), Diba Heydary, (diba.heydary), Oliver Trevett (oliver.trevett), Vivian He (vivian.he) @mail.utoronto.ca

Lectures and tutorials meet in-person; attendance is expected

First lecture: Friday, September 8

First tutorial: Week of September 18

First assignment due: Thursday, September 22

First midterm test: Thursday, October 12

If you are currently on the waitlist ...

... please attend lectures and tutorials. We will add you manually to the class roster on Quercus, so that you can submit assignments. All course information will be linked to the schedule

Course description: "A theoretical course in calculus; emphasizing proofs and techniques" [Arts & Science Calendar]. Topics include...

The real number line: Properties of the real numbers and how to construct them; upper and lower bounds; completeness; some useful inequalities
Functions: How to specify and represent a function; graphs; maxima, minima, and zeroes; continuity; derivatives and integrals; logarithm and exponential function, trigonometric functions
Infinite sequences and series: Convergence and limits; absolute convergence; power series and their radius of convergence
Proof-writing: Effective use of mathematical notation and verbal argument; proof techniques (complete induction; ε-δ formalism; contradictions and contrapositives)
Problem-solving skills: Constructing examples and counterexamples; calculating with confidence and purpose; making inequalities work for you; finding and correcting errors

Prerequisite: High school level calculus

Textbook: M. Spivak, "Calculus"

Evaluation:

20% : weekly assignments (due Thursdays 11:59pm on crowdmark; 19 in total, drop 4). A typical assignment has 6 problems, of which 2-3 will be marked

40% : four midterm tests (Thursday Oct. 12, Nov. 16, Jan. 18, and Feb. 29, 7-9pm, rooms TBD)

40% : final examination (to be scheduled by registrar)

We encourage you to discuss lectures and homework problems freely, work with fellow students, and consult available sources. Then write up your solutions individually, in your own words, and be ready to defend them! Your work will be judged on the clarity of your presentation as well as correctness and completeness. Late submissions are not accepted.

Absences. If you miss a substantial part of the course, please keep me updated. Absence Declaration Tool

Academic integrity statement. Consult the website Student Academic Integrity for information.

Accessibility. If you require accommodations for a disability, or have any accessibility concerns about the course, the classroom or course materials, please contact Accessibility Services as soon as possible: https://studentlife.utoronto.ca/department/accessibility-services/