Math 410-01, Problem
solving
techniques, Fall 2006

Syllabus

Syllabus

Instructor: Professor Junping
Shi |
Phone: 221-2030 email: jxshix@wm.edu |

Office: Jones
Hall 122 |
Office Hour: TThF
2-3:00pm or by appointment |

Plan
of the seminar

The structure of each meeting is as follows: first 20-30 minutes, the instructor will give a presentation on a mathematical topic, including main concepts and theorems, problem solving techniques, and a few typical examples to illustrate the theory; next 50-60 minutes, the class will discuss a problem set assigned prior week. Each week one problem set consiting of 7-10 problems will be assigned. Students should think about these problems before the class, and if you can solve some problems in the set, sketch your answer in notebooks, and try to present your answer in class. For each problem set, one problem will be assigned to each student, and he/she will lead the discussion of the problem, or present his/her solution.

The structure of each meeting is as follows: first 20-30 minutes, the instructor will give a presentation on a mathematical topic, including main concepts and theorems, problem solving techniques, and a few typical examples to illustrate the theory; next 50-60 minutes, the class will discuss a problem set assigned prior week. Each week one problem set consiting of 7-10 problems will be assigned. Students should think about these problems before the class, and if you can solve some problems in the set, sketch your answer in notebooks, and try to present your answer in class. For each problem set, one problem will be assigned to each student, and he/she will lead the discussion of the problem, or present his/her solution.

We
may have one or two take-home midterm "tests", similar to mathematical
competitions. You can think these tests as mock competitions. You will
be given a period of 4-5 days try to solve the problems. But the
results of the tests has no effect on your grade. Our "midterm exam" is
Virginia Tech competion in October 28,
Saturday, and our "final exam" is Putnam exam in December 2, Saturday.
Again, the results has no effect on your grade.

Grades

Your grade will mainly be determined by participation of discussions, and your presentations.

Resource

Resource for this seminar course is from (1) several books on this subject; and (2) internet. For the books, the instructor has now a collection of 6 books, and students in the seminar are welcomed to use these books for their need. For the internet resource, plese check the course website: http://www.math.wm.edu/~shij/math410-problem-solving/index.html

Textbooks and refererence books

There is no required textbook for the class. There are many good books on the subject of problem solving, and student can choose to pruchase one or more books for their interests. Recommended general problem solving books are

**Problem
Solving Through Problems ** By: Loren C. Larson

**Problem-Solving
Strategies (Problem Books in Mathematics)** By: Arthur Engel

**Mathematical
Olympiad Challenges** By: Titu Andreescu and Razvan Gelca

**Mathematical
Miniatures (New Mathematical Library) ** By: Svetoslav
Savchev, Titu Andreescu

**The
William Lowell Putnam Mathematical Competition 1985-2000: Problems,
Solutions, and Commentary** By: Kiran S. Kedlaya, et al

**The
William Lowell Putnam Mathematical Competition Problems and
Solutions: 1965-1984** By: Gerald L. Alaxanderson, et al

Topics and Schedule

Grades

Your grade will mainly be determined by participation of discussions, and your presentations.

Resource

Resource for this seminar course is from (1) several books on this subject; and (2) internet. For the books, the instructor has now a collection of 6 books, and students in the seminar are welcomed to use these books for their need. For the internet resource, plese check the course website: http://www.math.wm.edu/~shij/math410-problem-solving/index.html

Textbooks and refererence books

There is no required textbook for the class. There are many good books on the subject of problem solving, and student can choose to pruchase one or more books for their interests. Recommended general problem solving books are

Topics and Schedule

Week 1 (9/4) |
Problem set 1 | Pigeon
hole principle handout |

Week 2 (9/11) |
Problem
set 2 |
Mathematical induction |

Week 3 (9/18) |
Problem
set 3 |
Series, and sum
handout |

Week 4 (9/25) |
Problem
set 4 |
Congruence
handout |

Week 5 (10/2) |
Problem set 5 | Recurrence
handout |

Week 6 (10/9) |
Problem
set 6 |
Inequalities
handout |

Week 7 (10/16) |
no problem set, fall break |
Floor
function handout |

Week 8 (10/23) |
Problem
set 7 |
Polynomial
handout |

10/28 |
Va Tech Competition |
9:00-11:30am |

Week 9 (10/30) |
Problem
set 8 |
Probability
handout |

Week 10 (11/6) |
Problem
set 9 |
Binomial
coefficient handout |

Week 11 (11/13) |
Problem
set 10 |
Games, strategy,
puzzle handout |

Week 12 (11/20) |
Problem
set 11 |
Linear
Algebra handout |

Week 13 (11/27) |
||

12/2 |
Putnam Exam |
10am-1pm, 3-6pm |

Week 14(12/4) |
Review of Putnam problems |