## Math 101: Advanced Problem Solving

### Fall 2021

**Instructor:** Sucharit Sarkar.

**Class:** M 16:00-18:50, ROYCE 164.

**Textbook:** Titu Andreescu and Razvan Gelca,

Putnam and Beyond, ISBN 9780387257655.

**Useful
links:** CCLE,

MyUCLA,

Department
page,

Putnam
materials,

Putnam
information.

**Prerequisite:** Math 100 or significant experience with
mathematical competitions. Enrollment is by permission of the
instructor, based on the selection test or on past Putnam
results.

**Topics:** Advanced problem solving techniques and mathematical
topics useful as preparation for Putnam Competition. Problems in
abstract algebra, linear algebra, number theory, combinatorics,
probability, real and complex analysis, differential equations,
Fourier analysis. Regular practice tests given, similar in difficulty
to the Putnam Competition.

**Putnam:** MATH 101 is an advanced preparation course for
the

Putnam. (There
is an easier course for
Putnam, MATH 100, aimed at students not familiar with problem solving.)
These

Putnam materials may be useful for
Putnam prepration. The Putnam takes place on

2021-12-04, and you must

register for the Putnam examination before that.
There will be
an introductory preparation session, open to all students (whether or not enrolled in Math 101), on

2021-09-24 16:00-17:20 at Franz 1260. There will be a practice exam, open to all students, on

2021-09-27 16:00-18:50 at PAB 1434A, which also serves as a placement exam for MATH 101.
See

here for more information.

**Homework and exams:** Homework will be assigned every week and will be discussed in class; you should solve the
problems over the week, and will be asked to present the solutions in class. There will be four 3hr exams as
practice for Putnam. The first of these exams serves as a placement exam for MATH 101. (There will be no additional
exams during the Finals week).

**Grading:** Numerical grades will be recorded in the MyUCLA
gradebook and the composite numerical grade will be computed as 25%
for each of the four Putnam practice exams. Based on that, the final
grade (P/NP or letter grade) will be assigned. Since the test problems
are very hard, solving an average of 2/6 problems is enough for B+/A-;
lower and higher scores will correspond to lower and higher grades,
respectively. 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 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.

**Schedule:**
Date |
Time |
Location |
Activity |

2021-09-24 |
16:00-17:20 |
Franz 1260 |
Introductory session |

2021-09-27 |
16:00-18:50 |
PAB 1434A |
Practice test 1 (placement exam) |

2021-10-04 |
16:00-18:50 |
ROYCE 164 |
Discuss HW 1 |

2021-10-11 |
16:00-18:50 |
ROYCE 164 |
Discuss HW 2 |

2021-10-18 |
16:00-18:50 |
ROYCE 164 |
Practice test 2 |

2021-10-25 |
16:00-18:50 |
ROYCE 164 |
Discuss HW 3 |

2021-11-01 |
16:00-18:50 |
ROYCE 164 |
Discuss HW 4 |

2021-11-08 |
16:00-18:50 |
ROYCE 164 |
Practice test 3 |

2021-11-15 |
16:00-18:50 |
ROYCE 164 |
Discuss HW 5 |

2021-11-22 |
16:00-18:50 |
ROYCE 164 |
Discuss HW 6 |

2021-11-29 |
16:00-18:50 |
ROYCE 164 |
Practice test 4 |

2021-12-04 |
08:00-16:00 |
MS 6627 |
Putnam exam |