21-127 Concepts of Mathematics (Summer 1 2014)

Instructor: Sebastien Vasey
Office: Wean Hall 7108
Email: sebv (at) cmu (dot) edu
Office hours: Mon: 10AM-11AM, Wed: 6PM-7PM, Thu: 3PM-5PM, Fri: 10AM-11AM
Lectures: MTWRF 01:30PM-02:50PM WEH 4623

Grader: Ryan Murray
Office: Wean Hall 7209
Email: rwmurray (at) andrew (dot) cmu (dot) edu
Office hours: Tue: 3PM-5PM

News / Announcements

June 28, 2014: Solution to the final is up. Course grades will be posted on SIO. This webpage will not be maintained anymore (but the notes will). Thank you all and enjoy the rest of the summer.
June 26, 2014: Solution to the sample final has been posted.
June 24, 2014: Assignment 10 is out. Please read the instructions at the beginning.
June 22, 2014: The final will take place on Friday June 27th in class from 1h30 to 2h50 pm. A practice exam and even more exercises have been posted. The notes have also been updated with the chapter on probability.
June 20, 2014: Assignment 9 is out.
June 17, 2014: Assignment 8 is out. Note that problem 4 is different than in the printed version handed out in class.
June 15, 2014: The notes contain the first number theory lecture. The schedule has also been updated, and some additional exercises for week 5 have been posted. Assignment 7 has been updated to make the statement of the problem with the numbers on a circle clearer.
June 13, 2014: Assignment 5 has been graded. Assignment 7 (and some additional problems) is available.
June 11, 2014: The midterm has been graded and can be picked up in class or at my office hours. The average was about 67.
June 8, 2014: Solution to the sample midterm is online. The sample problems for week 2 have also been updated. Note that 5(g) was wrong and has been changed.
June 6, 2014: Assignment 4 has been graded and can be picked up whenever you see me. I will hold additional office hours on Sunday June 8, 2014 from 5pm to 7pm.
June 4, 2014: Due to a typo in the statement of problem 4.1, Assignment 5 has been updated. You should replace "a = b" by "a = c" and "b = c" by "b = d".
June 3, 2014: Assignment 5 is out.
June 1, 2014: Updated schedule and notes, and added additional exercises as well as a sample midterm for practice.
May. 30, 2014: Assignments 1 and 2 have been graded and can be picked up during lecture or my office hours. Solutions can also be picked up. Assignment 4 will be out shortly.
May. 27, 2014: Assignment 3 is out.
May. 26, 2014: Office hours have been posted.
May. 23, 2014: Posted Assignment 2.
May. 6, 2014: This webpage is online, hurray! Please read the Course syllabus.

Lecture notes

I am writing my own lecture notes for the course. They are no substitute for attending lectures, but you are advised to read them as the course goes on.

You can download them from here: Lecture notes.

They are a work in progress and will be updated many times throughout the semester. If you see a mistake or a typo, please let me know (you may even get some extra credit).

Assignments

Assignments will be posted here.

Assignment 1 (due Friday, May 23).
Assignment 2 (due Wednesday, May 28).
Assignment 3 (due Friday, May 30).
Assignment 4 (due Tuesday, June 3).
Assignment 5 (due Friday, June 6).
Assignment 6 (due Friday, June 13).
Assignment 7 (due Tuesday, June 17).
Assignment 8 (due Friday, June 20). Note that problem 4 is different from the printed version handed out in class.
Assignment 9 (due Tuesday, June 24).
Assignment 10 (due Thursday, June 26). Note that there are instructions at the beginning of the assignment: you only have to do three problems.

Practice exercises

The following are additional exercises that are completely optional. They range from very easy to very hard, and are listed in no particular order. Please ask me if you get stuck on one of them, or need solutions.

You can also practice on a sample midterm.

Here is a sample final.

Other resources

An introduction to proofs and the mathematical vernacular: Notes from a similar course taught by Martin V. Day.
John P. D'Angelo and Douglas B. West, Mathematical thinking: problem-solving and proofs. 2nd ed., Prentice Hall, 2000.
Michael Spivak, Calculus. 4th edition., Publish or Perish, 2008 (Recommended if you want to see how one can get to calculus and real analysis from the facts about the reals seen in class. Also has many exercises. An older edition is available from the CMU Library).
Numberphile has short, to the point, lectures on: