BU




C O N C E P T S    O F    M A T H E M A T I C S  -  S U M M E R  II   2 0 1 5 


LECTURES: Monday, Tuesday, Wednesday, Thursday, Friday 9:00am-10:20am, in Porter Hall A18A

INSTRUCTOR: Solesne Bourguin, office hours Tuesday, Wednesday, Friday 11:30am-12:30pm, you also can email me (bourguin@math.cmu.edu) to set up an appointment or just drop by (Wean Hall 8206).

GRADER: Nate Ince, office hours Tuesday, Friday 1:00pm-2:00pm in Wean Hall 6203.

COURSE DESCRIPTION: The aim of the course is to introduce proof-based mathematics. In mathematics, saying that a statement is true means something very precise: there is an unambiguous argument, a proof, which explains why the statement is true. This course will focus on the study and writing of such proofs in various fundamental mathematical topics such as logic and set theory, combinatorics, number theory and probability theory, which are central to further mathematical practice and also crucial in computer science and engineering.

PREREQUISITES: There are no formal prerequisites. However, basic notions of algebra and arithmetic would be helpful.

TEXTBOOK: There is no required textbook for this class. Lecture notes written by Sebastien Vasey (download) can be used to complement to lectures in class. Here are some other optional resources:


GRADING: problem sets (30%), midterm (30%) and a final exam (40%).

HOMEWORK: The problem sets will be posted on this website. The homework will be collected at the beginning of class on the due dates. Make sure to put your last and first names on your paper as well as your andrew ID. Late homework will not be accepted. The homework schedule is included in the tentative schedule (see below).

PROBLEM SETS.
Problem set 1 (due on Monday, July 6th).
Problem set 2 (due on Thursday, July 9th).
Problem set 3 (due on Monday, July 13th).
Problem set 4 (due on Thursday, July 16th).
Problem set 5 (due on Monday, July 20th).
Problem set 6 (due on Thursday, July 23rd).
Problem set 7 (due on Monday, July 27th).
Problem set 8 (due on Thursday, July 30th).
Problem set 9 (due on Monday, August 3rd).
Problem set 10 (due on Thursday, August 6th).

ADDITIONAL MATERIAL.
Review session one (before midterm exam).
Niraj Khare's lecture slides (lecture of 07/22/2015).
Review session two (before final exam).

TENTATIVE SCHEDULE: