Math 145 Course Description

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Math 145. Problem solving. Fall 2005.

Prerequisite: Math 76.

Hours: 3.

There is no (published) text for this course. A draft of a book being currently prepared by the instructor will be provided. Also, you can download it by clicking here (contains solutions to odd numbered problems in the first few chapters; solutions to later chapters will be posted later)

Content: Topics to be covered include: logic, types of proofs, principle of mathematical induction, Dirichlet's box principle (also called pigeonhole principle), number theory, case study, invariants, coloring proofs, working backwards, geometry, mathematical games and algorithms, non-routine calculus problems, problems from math olympiads and journals. More topics may and probably will be added later. Students will be asked to present their solutions on the board. Working in groups is encouraged. The purpose of this class is to learn to solve non-standard problems, and also to write your proofs in a complete and correct way.

See also the Catalog Description.

Course objectives
Upon completion of this course, students should know/understand:

Importance of a formal (rigorous) proof
Meaning of logical operations (and, or, negation, implication) and quantifiers (universality and existence)
Difference between different types of proof (direct, by contradiction, by contrapositive, by example/counterexample, etc.)
Principle of Mathematical Induction
Dirichlet's Box Principle
Divisibility properties of integer numbers; congruences
The concept of invariant
Basic graph theory terminology (vertex, edge, degree of a vertex, etc.)

Learning outcomes
Upon completion of this course, students will be able to do:

Translate word problems into mathematical equations and relations
Recognize problems which can be solved using one of the following techniques:
- Dirichlet's Box Principle
- Mathematical Induction
- Divisibility and/or Congruences
- Case Study
- Patterns
- Invariants
- Coloring
- Symmetry
- Graphs
- Working backwards
Set up and solve appropriate equations for solving calculus problems involving slopes and areas.

Grading policy: Your grade for the course will be based mostly on your performance on exams and homework (more information on these below). You will also receive points for submitting solutions of problems to jounals, class presentations, and inventing new problems. The number of points awarded for these are shown below. In addition, extra credit will be given for finding mistakes/typos in the book and handouts.

Test 1	50 points
Test 2	50 points
Test 3	50 points
Final exam	100 points
Homework	250 points
Total	500 points
Extracurricular activities: Submissions of solutions to journals Class presentations Writing new problems	up to 50 extra points

Perhaps a few words have to be said about the extracurricular activities mentioned above. During the semester, I will bring a few journals with problems that you should try to solve. If you succeed, write your solution and show to me. Depending on correctness/completeness of your solution and difficulty of the problem, you can get up to 10-15 points for your solution. If it is correct and complete, you should send your solutions to the journal (and may be your solution will even be published!) You can also present your solution in class and get up to 5 points for your presentation. (Note: in case of team work, the presenters will share the points.) Also, you are invited to propose problems for a competition for high school students... more about this in class. Depending on originality of your problems, you will get 1-3 points for each. Finally, extra credit will be given for finding mistakes/typos in the book (if you are the first one to report a mistake).

Points earned	grade
425-500	A
350-424	B
275-349	C
200-274	D
0-199	F

Exams: There will be three hour tests and one final comprehensive exam. If for any reason you can not take a test at the scheduled time, please let me know as soon as possible, and certainly before the test. See schedule for exam dates.
Solutions to past exams will be posted here in the future.

Class attendance is strongly encouraged. In addition to new material, important course information will be given in class, often various handouts will be given.

There will be weekly homework due Friday at 12 pm covering the material of the preceding week. Please bring your homework to class. We will sometimes discuss homework in class, so no late papers will be accepted unless you are sick or have another serious reason to miss the class.

Extra Help: It is essential not to fall behind, because each class may use the material studied previously. If you have trouble with some material, seek help in the following ways:

Ask me, either in class or privately. My contact info is given on the course web page. Don't be shy to ask questions. If you don't understand something, chances are very high that somebody else doesn't understand that either. In particular, you are more than welcome to ask questions about solutions in the book. But I will not help you with the homework problems. Those are for you to solve. Remember, the purpose of this class is for you to learn to solve non-routine problems. However, if you'd like to know a solution to a homework problem after it's due, let me know, and we'll discuss the problem in class.
Work with your classmates. Note: working on your homework together is allowed, however, every student should write down their solutions on their own. Also, if you have worked with someone, please indicate that on your paper.

If you are having any difficulties, seek help immediately - don't wait until it is too late to recover from falling behind, or failing to understand a concept!

Students with disabilities: upon identifying themselves to the University, students with disabilities will receive necessary accommodation for learning and evaluation. For more information, see http://studentaffairs.csufresno.edu/ssd

Academic honesty: cheating and plagiarism will not be tolerated in this class. For information on the University's policy, see the University Catalog (section Policies and Regulations).

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This page was last revised on September 15, 2005.