## Math 100: Problem Solving

### Fall 2022

**Instructor:** Sucharit Sarkar.

**Class:** MWF 12:00-12:50, MS 6627.

**Office hours:** M 13:30-14:30 15:00-15:30, MS 6909.

**Reader:** Gary Song

**Textbook:** Loren Larson,

Problem Solving Through Problems, ISBN 9780387961712.

**Additional reading:** Titu Andreescu and Razvan Gelca,

Putnam and Beyond, ISBN 9780387257655.

**Useful
links:** MyUCLA,

Department
page,

Putnam
materials,

Putnam information.

**Prerequisite:** The official prerequisite is MATH 31A. However,
MATH 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 small quiz. 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:** MATH 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. 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.

**Schedule:** We will try to follow the schedule from
the

Department
page.

**Putnam:** MATH 100 can serve as basic preparation for the

Putnam for students who had minimal exposure to
problem solving. (There is a more intensive preparation course for Putnam, MATH 101 (offered every alternate year),
aimed at students who are already familiar with problem solving.) These

Putnam materials
may be useful for Putnam prepration.
See

here for more information.

**Homework:** Homeworks are due at the beginning of lecture on Wednesday; submit paper copies of homeworks in class; do not submit homework by e-mail. Late
homeworks will not be accepted; however, your lowest homework score will be dropped when computing your grade.

HW |
Due on |
Problems |

1 |
2022-10-05 |
HW1 |

2 |
2022-10-12 |
HW2 |

3 |
2022-10-19 |
HW3 |

4 |
2022-10-26 |
HW4 |

5 |
2022-11-02 |
HW5 |

6 |
2022-11-09 |
HW6 |

7 |
2022-11-16 |
HW7 |

8 |
2022-11-23 |
HW8 |

9 |
2022-11-30 |
HW9 |

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 |
Syllabus |

Quiz |
MS 6627 |
2022-10-05 |
12:00-12:50 |
Chapter 2 |

Midterm |
MS 6627 |
2022-10-26 |
12:00-12:50 |
Chapters 2,3,4,7 |

Final |
MS 6627 |
2022-12-06 |
08:00-11:00 |
Chapters 1-8 |

Old
finals:

2015,

2016,

2017.

There will be no make-up exams. Submitting 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; you will pass if your composite numerical score is more
than 60%.

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. 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.