Welcome to the problem seminar and let’s have fun with mathematics! Our intention is to have a great time while expanding our mathematical horizons in a challenging way. Basically, we give you problems — many, many problems — and you solve a few of them. In class, solutions are presented or problems are discussed with the aim of working toward solutions. The problems will resemble the style of problems on the Math Olympiad or Putnam exam, with very basic prerequisites — MATH 1122, 1132, 121, 1152, 2142 — but sometimes involve difficult tricks. We will try to rotate topics to cover as many problem-solving tricks as possible.

**Even if you are not registered for this class, you are welcome to attend the lectures.**

**This year’s Putnam Competition will be held on Saturday, December 3rd.** This course should be good preparation for that. Most, if not all, of you should plan to take the Putnam. It is in no way required, but is a good way to cap the semester’s problem-solving experience.

### Course Organizers

- Vasileios Chousionis MONT 325 vasileios.chousionis@uconn.edu
- Ovidiu Munteanu MONT 434 ovidiu.munteanu@uconn.edu
- Liang Xiao MONT 235 liang.xiao@uconn.edu

### Grading scheme

There will be 7 homeworks assigned after the meetings. You must submit your solutions before the next meeting. No extension will be given. The highest score on each homework is 20 points, so the total is 140 points. The letter grade of the class will be based only on your homeworks. The following table lays out the conversion.

- A 100 and up; B 80-100; C 60-80; D below 60.

Each homework consists of 10-20 problems. Each problem is labeled with a number from 1 to 10 indicating the difficulty: 1 is easy, 4 is at the level of Putnam A1-A2-B1-B2, and 8 is at the level of Putnam A3-A4-B3-B4. Of course, remember that this is a subjective measurement.

Each problem will be graded by correctness from 0 to 3. The total points earned for a problem is the product of its difficulty and correctness. The score of each homework cannot exceed 20 points, but you are always welcome to do more.

You can work together on the problems, but unlike in many other courses, we do not particularly encourage you to do so. In any case, you need to write up the solution on your own.

### Course Schedule

We will meet 9 times this semester, all on Tuesdays 4:00-5:30 PM in MONT 414. Here is a list of dates and topics.

Dates | Instructor | Topic | Homeworks |

August 30 | Liang Xiao | Number Theory | Problem set 1 |

September 6 | Liang Xiao | Summation and Iteration | Problem set 2 |

September 20 | Ovidiu Munteanu | Induction | problem set 3 |

October 4 | Ovidiu Munteanu | Linear algebra | problem set 4 |

October 18 | Vasileios Chousionis | Calculus I | problem set 5 |

November 1 | Vasileios Chousionis | Calculus II | problem set 6 |

November 15 | Tom Roby | Generatingfunctionology | problem set 7 |

November 29 | (Canceled due to conflict with an important faculty meeting) | ||

December 3 | Putnam Competition 2016 | ||

December 6 | Putnam 2016 discussion |

### Useful Resources

- Kiran Kedlaya keeps a list of past Putnam problems here (after 1985)

### Past Putnam Competition Results

#### 2015 Putnam Competition

- Team rank: 60
- top scores at UConn: 1. Patrick Adams (top 500 nationwide); 2. Lindsay Cadwallader; 3. Timothy Smits.

#### 2014 Putnam Competition

- Team rank: 85
- top scores at UConn: 1. Daniel O’Connell (top 500 nationwide); 2. Patrick Adams; 3. Lindsay Cadwallader, Nicole Chubet, Neil Dokurno, Elizabeth Lauri.