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 course should be good preparation for the Putnam Competition on December 2, 2017. Most, if not all, of you should plan to take the competition. It is in no way required, but is a good way to enhance your problem-solving experience. Also, there will be an annual calculus competition to be held in the spring semester.

### Course Organizers

- Vasileios Chousionis MONT 325 vasileios.chousionis@uconn.edu
- Aurel Mihai Fulger MONT 323 aurel.fulger@uconn.edu
- Ovidiu Munteanu MONT 434 ovidiu.munteanu@uconn.edu
- Liang Xiao MONT 235 liang.xiao@uconn.edu

### Grading scheme

There will be 6 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 120 points. The letter grade of the class will be based only on your homeworks. The following table lays out the conversion.

- A 90 and up; B 75-90; C 60-75; 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 6 or 7 times this semester, all on** Tuesday 4:00-5:30 PM** in room **MONT 414**. Here is a list of tentative dates and topics.

Dates | Instructor | Topic | Homeworks |

September 5 | Liang Xiao | Recurrence and sequences | Homework 1 |

September 12 | Liang Xiao | Number Theory | Homework 2 |

September 26 | Ovidiu Munteanu | Matrices and Determinants | Homework 3 |

October 17 | Ovidiu Munteanu | Inequalities | Homework 4 |

October 24 | Vasileios Chousionis | Calculus I | Homework 5 |

November 7 | Vasileios Chousionis | Calculus II | Homework 6 |

November 28 | Mihai Fulger | TBA | |

December 2 | Putnam Competition 2017 |

### Useful Resources

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

### Past Putnam Competition Results

#### 2016 Putnam Competition

- Team rank: 49
- Top scores at UConn: 1. Timothy Smits; 2. Patrick Adams, Surath Fernando, Vyas Krishnamurty; 3. Lindsay Cadwallader, Ellizabeth Lauri.

#### 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.