## Math 100: Problem Solving

### Fall 2017

**Instructor:** Sucharit Sarkar.

**Class:** MWF 10-10:50am, MS 6221.

**Office hours:** 1-3pm, MS 6909.

**Exceptions:** 11am-2pm on
11/1 instead of 11/3; 9-11am, 12:30-3pm on 12/11.

**Reader:** Ken Willyard.

**Textbook:** Loren Larson (L),

Problem Solving Through Problems, ISBN 9780387961712.

**Additional reading:** Titu Andreescu and Razvan Gelca (AG),

Putnam and Beyond, ISBN 9780387257655.

**Useful links:** University
page,

MyUCLA,

Putnam materials.

**Prerequisite:** The official prerequisite is MAT 31A. However,
MAT 100 is aimed at the most talented students at UCLA, and you should
only take it if you got A's in your lower division math
classes. Freshmen and transfer students who have some experience in
math contests are welcome to enroll. To help you decide if the course
is right for you, we will have a 25 minute long quiz in class on
10/6. Based on the results of the quiz, I will give you a
non-binding recommendation about whether you should continue in the
class. The quiz does not count toward your course grade.

**Topics:** MAT 100 is a course in problem solving. The problems
are more varied and unexpected than in a typical undergraduate
mathematics course. Often an original or imaginative step is
required. The course can serve as basic preparation for the
Putnam. Topics to be covered include: Induction, the pigeonhole
principle, inequalities, modular arithmetic, closed form evaluation of
sums and products, problems in combinatorics, probability, geometry,
rational functions and polynomials, and calculus.

**Homework:** Homeworks are due at the beginning of lecture on
Monday. (

**Exceptions:** HW9 is due at the beginning of lecture on
12/6.) Do not submit homework by e-mail. No late homework will be
accepted. However, your lowest homework score will be dropped when
computing your grade.

You are encouraged to work in groups on your homework; this is
generally beneficial to your understanding and helps you learn how to
communicate clearly about mathematics. However, you must write up all
solutions yourself. Moreover, since crediting your collaborators is an
important element of academic ethics, you should write down with whom
you worked at the top of each assignment. You should also cite any
sources (other than lectures and the textbook) that you use.

**Exams:** The exams are non-collaborative closed-book exams. You
are not allowed to use books, notes, or any electronic devices (such
as calculators, phones, computers) during the exams. There is a single
quiz, a single midterm, and a single final exam on the following
dates.

Exam |
Location |
Date |
Time |

Quiz |
MS 6221 |
10/6 |
10-10:25am |

Midterm |
MS 6221 |
11/3 |
10-10:50am |

Final |
MS 6221 |
12/13 |
11:30am-2:30pm |

Old
finals:

2015,

2016.

There will be no make-up exams. Attending the final exam is
mandatory. In particular, note that university policy requires that a
student who misses the finals be automatically given F, unless the
absence is due to extreme and documented circumstances, in which case,
if the performance in the course is otherwise satisfactory, the grade
might be I.

**Grading:** Numerical grades will be recorded in the MyUCLA
gradebook and the composite numerical grade will be computed as 20% HW
+ 30% Midterm + 50% Final. Based on that, the final grade will be Pass
or No Pass.

If you believe a problem on a homework or an
exam has been graded incorrectly, or that your score was not correctly
recorded in the MyUCLA gradebook, you must bring this to the attention
of the instructor within 10 calendar days of the due date of the
assignment in question, or the date of the exam, and before the end of
the quarter (12/15). Grading complaints not initiated within this
period of time will not be considered. Please verify in a timely
manner that your scores are correctly recorded on MyUCLA.

**Tentative schedule:**
Week |
Topic |

1-2 |
L 2, AG 1 |

2-3 |
L 7.1-7.4, AG 2.1 |

3-4 |
L 3, AG 5 |

4-5 |
L 4, AG 2.2, 2.4 |

5-6 |
L 5.2-3, AG 3.1 |

6-7 |
L 1.3, 5.1, AG 6 |

7-8 |
L 5.4, AG 6.2-3 |

8-9 |
L 8, AG 4 |

9-10 |
L 6, AG 3 |