Ideas in Mathematics (Math 170-002, Fall 2014, UPenn)
Aug 20, 2014
Hours and Location
Lectures: Monday, Wednesday and Friday, 9-10am. Location: DRL room A5. (Total number of lectures: approx. 35)
Recitations: Tuesday and Thursday (please check your respective schedules for the exact hours and locations).
Lectures start on Aug 27 (Wednesday). Last lecture on Dec 8 (Monday). (Review session on Dec 10)
List of days without lectures: Sept 1 (M), Oct 10 (F),
Oct 24 (F), Nov 28 (F)
First mid-term: September 29 (Monday), during the usual lecture hour.
Second mid-term: November 3 (Monday), during the usual lecture hour.
Final exam: December 15 (Monday), 9-11am (http://www.upenn.edu/registrar/finals/index.html)
Office location: DRL 3C7
Office hours: Fridays 1-2pm (or by appointment)
Office hours: Mondays and Tuesdays 2-3pm
- "Book of Proofs" (2nd Edition) by Richard Hammack.
- "The Heart of Mathematics: An invitation to effective thinking" (4th Edition) by Edward B. Burger and Michael Starbird. (Chapters 2-6)
Attendance, Homeworks and Exams
- Attendance and participation in class is expected.
- There will be weekly homeworks assigned on Wednesdays, and due on the following Wednesday at the beginning of class. You can discuss among yourselves on the homework problems. But each of your homework submission must be your original work.
- There will be a few surprise quizzes, either during the lecture hours or during the recitation hours.
- There will be three exams: two mid-terms and one final. The first mid-term will tentatively take place around end of September, and the second mid-term around the end of October.
- The homeworks and announcements will be posted on the canvas site. So make sure you are signed up there and regularly check the announcements: https://canvas.upenn.edu/courses/1255759
Class participation: 5%
Homeworks and Quizzes: 25%
Midterm 1: 20%
Midterm 2: 20%
Elementary Set theory (2-3 lectures)
- Set theory.
- Venn diagram.
Logic and Methods of proof (3-4 lectures)
- Statements in mathematics.
- Methods of proof.
Numbers (4-5 lectures)
- Types of numbers, number theory.
- Introduction to complex numbers.
Elementary Topology (5-6 lectures)
- Concepts and examples from topology.
- Topological invariants (Euler's characteristics).
- Three and higher dimensional spaces.
Elementary graph theory (4-5 lectures)
- Definition and description of graphs.
- Elementary computations.
- Elementary graph algorithms.
Geometry - Distances (4-5 lectures)
- Introduction to Metric and their various types.
- Introduction to higher dimensional measures (area, volume).
Geometry - Symmetry and Measures (4-5 lectures)
- Symmetry, Platonic solids.
- Canvas: https://canvas.upenn.edu/courses/1255759.
- University's list of important dates: http://www.upenn.edu/almanac/3yearcal.html.