Class: MWF 12:00-12:50 in Altgeld Hall 159

and MWF 3:00-3:50 in the Henry Administration Building room 154

Office hours: Mon 10:00-11:00, Tue 15:00-16:00 and Wed 20:00 -21:00 in the Espresso Royale in the Illini Union

The textbook is Mathematical Thinking: Problem-Solving and Proofs by John P.D'Angelo and Douglas B. West.

Homework policy: You are not allowed any late homework. You will however be allowed to drop your lowest scoring homework for the computation of the final grade.

What? | Due date | Comments | Percentage | median | mean | standard derivation |

Homework | weekly, due Friday | Solutions for last year's Midterm 1 and problem set 5 are now accessible on last year's web-page. Some more solutions are below. | 40% | |||

First midterm (take-home part) | Friday, October 13th | Midterm 1 and Solutions | 13% | |||

First midterm (in-class part) | Friday, October 13th | Solutions, Last year's Midterm 3, Last year's inclass final. Read Chapter 1-3, the solutions of the problem sets. | 7% | |||

Second midterm (take-home part) | Friday, November 17th | Midterm 2 | 13% | |||

Second midterm, in-class part | Friday, November 10th | 7% | ||||

Final, take-home part | Final | 13% | ||||

Final, in-class part | Dec 12th or 15th, 7-10pm | 7% |

In order to check your scores on-line, go here.

Each of the exams will consist of a take-home and an in-class part. The final will cover the material of both midterms. If you do better on the final part for midterm n than you did in midterm n itself, you may replace the midterm n score by the score in the part of the final corresponding to midterm n. Letter grades will only be computed at the very end of the term, and as follows:A | A- | B+ | B | B- | C+ | C | D | F |

85-100 | 80-84 | 75-79 | 70-74 | 65-69 | 60-64 | 55-59 | 50-54 | 0-49 |

Lecture | Date | Summary | Assignments | Suggested reading |

1 | 08/23 | Administrative issues. Group work on selected problems. (Here the solutions.) | Prepare to present your group's progress to the class. | |

2 | 08/25 | Presentation and discussion of group work problems. | Write a formal proof for Problem 1. | |

3 | 08/28 | Elementary set theory | The chapter about sets | |

4 | 08/30 | Language and proofs - truth tables | The chapter about language and proofs | |

5 | 09/01 | Language and proofs - quantifiers and negating statements | Chapter 2 | Problem Set 2 solutions |

6 | 09/06 | Language and proofs, negating statements | ||

7 | 09/08 | More on negations; relations and maps | Chapter 1, Wikipedia on de Morgan's Laws and propositional logic | Problem Set 3 due Friday Sept 15 solutions.) |

8 | 09/11 | Injective and surjective maps, students questions on Problem Sets 2 and 3. | Book, p.83 | |

9 | 09/13 | Continuation of Monday's discussion, induction. | ||

10 | 09/15 | Induction. | ||

11 | 09/18 | Group work on induction. | ||

12 | 09/20 | Bijections. There is a bijection between two finite sets if and only if the two sets have the same number of elements. Cardinality. | ||

13 | 09/22 | Bijections from the natural numbers to the even numbers, to the odd numbers. Proof that X is countable if and only if X is a union of an increasing sequence of finite sets. A bijection from N x N to N. | ||

14 | 09/25 | Epsilon-delta proofs - how to systematically organize a straightforward proof. | Problem Set 4 solutions more solutions | |

15 | 09/27 | Injective maps have left-inverses. How to systematically organize a straightforward proof (continued). | ||

16 | 09/29 | Injective maps have left-inverses (continued). Questions about Problem Set 4. | Problem Set 5 | |

17 | 10/02 | Induction: group work on the lions problem | All of Chapter 3 | |

18 | 10/04 | The lions continued. | ||

19 | 10/06 | Review, the handshake problem | Book, 3.26. | Midterm 1 |

22 | 10/13 | In-class test | Problem Set 6 | |

23 | 10/16 | review of set theory | ||

24 | 10/18 | review set theory | ||

25 | 10/20 | review | ||

26 | 10/23 | modular arithmetic | ||

27 | 10/25 | modular arithmetic | ||

28 | 10/27 | modular arithmetic | Problem Set 7 | |

29 | 10/29 | monsters | ||

30 | 11/1 | monsters, finding inverses in modular arithmetic | ||

31 | 11/3 | Groups, statement of Fermat's little theorem | Problem Set 8 | |

32 | 11/5 | Groups | ||

33 | 11/7 | Groups, review on set-theory and logic | ||

34 | 11/10 | in-class exam | If you want to read more about propositional logic, try the first chapter of Kenneth H. Rosen's book on Discrete Mathematics (it is on reserve in the math library). | |

35 | 11/13 | groups, subgroups, cosets | ||

36 | 11/15 | The order of a subgroup divides the order of the group | ||

37 | 11/17 | order of subgroup divides order of group (ctd). Fermat's little theorem. | ||

38 | 11/27 | Homework from the book: Exercise A.7.; prove the statement in exercise 13.11. a); prove the statement in exercise 14.8. a) |