Ideas in Mathematics (Math 170-001, Fall 2015, UPenn)
Aug 16, 2015
Hours and Location
Lectures: Tuesdays and Thursdays, 10:30am - noon (1.5 hours each).
Lecture Location: DRL room A2.
Recitations: Mondays & Wednesdays, 8am-9am & 9am-10am (please check your respective schedules for the exact hours and locations).
- Lectures start on Aug 27. Last lecture on Dec 8. (Total number of lectures: approx. 23)
- List of days without lectures: Oct 8 (Fall Break), Nov 26 (Thanksgiving)
- Drop Period ends: Oct 9. Last day to withdraw from a course: Nov 6.
- First mid-term: Oct 1 (Thursday), 10:30am. (It will be a ~45min exam starting at 10:30am during the usual lecture time and location. The exam will be followed by usual lecture for the remaining time of the class.)
- Second mid-term: Oct 29 (Thursday), 10:30am. (It will be a ~45min exam starting at 10:30am during the usual lecture time and location. The exam will be followed by usual lecture for the remaining time of the class.)
- Final exam: Dec 15, 9-11am (See http://www.upenn.edu/registrar/finals/index.html for details.)
Office location: DRL 3C7
Office hours: Fridays 1-2pm (or by appointment)
E-mail: See canvas page
Office location: See canvas page
Office hours: Monday 5:30-6:30, Wednesday 11am-12pm
- "Book of Proofs" (2nd Edition) by Richard Hammack.
- Only as reference: "The Heart of Mathematics: An invitation to effective thinking" by Edward B. Burger and Michael Starbird. (Chapters 2-6)
- Notes provided in class:
Attendance, Homeworks and Exams
- Attendance and participation in class is expected. You are expected to attend every lecture and recitation. In case you miss a lecture, you will need to figure out what was covered in that class either by talking to your fellow students, or by stopping by my office hours. It is your responsibility that you do these to catch up with the class.
- There will be weekly homeworks assigned on Wednesdays, and due on the following week's Thursdays 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/1293744
- Late homework submissions will NOT be accepted. This is so that we can ensure a smooth flow in the grading of the homeworks (avoid backlogs) and to ensure uniformity and fairness. Likewise, if you miss a surprise quiz, NO make-up quiz will be allowed. Exams dates will be announced well in advance. So, if you miss an exam, NO make-up exam will be allowed either.
- Conditions for exceptions on late submissions and make-up quiz/exams: Late submission of homeworks will be allowed only if you obtain and send an official course absence report (on medical grounds or otherwise) from the university in advance, reporting your absence during the period in which the homework was assigned. For make-up quiz or make-up exam (on serious medical grounds or emergencies), in addition to sending an official course absence report, you'll also need to have an email sent to me by your academic advisor confirming your valid/serious reason of absence. No other form of letter/certificate will be accepted.
Class participation: 5%
Homeworks and Quizzes: 25%
Midterm 1: 20%
Midterm 2: 20%
Course Outline (Subject to Change)
Elementary Set theory (1-2 lectures)
- Set theory.
- Venn diagram.
Logic and Methods of proof (2-3 lectures)
- Statements in mathematics.
- Methods of proof.
Numbers (3-4 lectures)
- Counting (elementary combinatorics).
- Types of numbers, number theory.
- Introduction to complex numbers.
Elementary Topology (3-4 lectures)
- Concepts and examples from topology.
- Topological invariants (Euler's characteristics).
- Three and higher dimensional spaces.
Elementary graph theory (2-3 lectures)
- Definition and description of graphs.
- Elementary properties and computations.
Geometry - Distances (3-4 lectures)
- Introduction to Metric and their various types.
- Introduction to higher dimensional measures (area, volume).
- Measuring distances on different surfaces.
Geometry - Symmetry and Measures (2-3 lectures)
- Symmetry, Platonic solids.
- Canvas: https://canvas.upenn.edu/courses/1293744.
- University's list of important dates: http://www.upenn.edu/almanac/3yearcal.html.
- Fall 2015 Course Timetable: http://www.upenn.edu/registrar/timetable/math.html.
- Fall 2015 Room Roster: http://www.upenn.edu/registrar/roster/math.html.