Cezar Lupu

Home » Uncategorized » The Putnam seminar, Fall 2016, University of Pittsburgh

The Putnam seminar, Fall 2016, University of Pittsburgh

Information about the competition and seminar (course description)

The William Lowell Putnam Mathematical Competition is the premiere competition for undergraduate students in North America. More than 500 universities compete in this contest organized by the Mathematical Association of America (MAA).  The competition takes place in the FIRST Saturday of December. This year’s Putnam competition will be held on Saturday, December 3 in Thackeray 703 or 705, from 10.00 am-1.00 pm and 3.00 pm-6.00 pm. The test is supervised by faculty members of each participating school. Every problem is graded on a scale of 0-10. The problems are usually listed in increasing order of difficulty, with A1 and B1 the easisest, and A6 and B6 the hardest. Top 5 scoring students on the Putnam exam are named Putnam Fellows. A student can take this exam maximum four times and the Putnam official team of the university consists of 3 members.
 The purpose of this class is to provide a comprehensive introduction into the world of problem solving in different branches of mathematics such as: real & complex analysis, linear algebra, abstract algebra, combinatorics, probability, geometry and trigonometry and number theory.
The teaching style will be a mixture of a lecture and a problem-solving session. By the end of this course, students should develop fundamental problem solving skills, and become accustomed to concentrating on a problem for an extended period of time. Indeed, this seminar concentrates on the raw creative problem-solving skills which can serve as an essential ingredient in almost every field of activity.  On the other hand, starting this Fall, the Putnam seminar has honors designation.
Last year, Pitt official Team ranked 24th in the nation and this marks the best performance since 2002. More details about this can be found here and here.

Course number, lecturers and webpage
Schedule and locations
  • Tuesday, 5.15-7.00 PM in Thackeray Hall, room 427

This is a lecture given by the instructor on a certain topic. The students will learn different concepts and techniques. Moreover, the lecturer will also present solutions of some problems and will assign other problems as homework for the students.

  • Thursday, 5.15-7.00 PM in Thackeray Hall, room 703 

This is more like a recitation rather than a lecture. The students will meet and discuss with the coordinators the problems assigned by the lecturer as homework.

Detailed program (lectures & recitations)

Week 1. What is Putnam competition? Organizational meeting

Abstract: This is an introduction to the seminar and the competition itself. There will be discussed training techniques for a competition of this caliber.

Lecturers: George Sparling & Cezar Lupu
Date: September 8


Week 2. (Elementary) Algebra

Abstract: This seminar will cover problems on topics such as algebraic identities and inequalities as well as polynomials in one variable.

Lecturer: Cezar Lupu
Date: September 13

Recitation instructor: Cezar Lupu
Date: September 15


Week 3. Real Analysis I

Abstract: This will cover problems on topics such as sequences of real numbers, convergence, limits and series of real numbers.

Lecturer: Cezar Lupu
Date: September 20

Recitation instructor: Cezar Lupu
Date: September 22


Week 4. Geometry and Trigonometry

Abstract: This will cover problems on topics such as vectors, conics, quadratics, and other curves in the plane as well as trigonometric formulae.

Lecturer: Derek Orr
Date: September 27

Recitation instructors: George Sparling & Cezar Lupu
Date: September 29


Week 5. Abstract Algebra

Abstract: This will cover problems on topics such as groups, rings, and finite fields.

Lecturer: George Sparling
Date: October 4

Recitation instructor: George Sparling
Date: October 6


Week 6. Real Analysis II

Abstract: This will cover problems on topics such as continuity and differentiability of functions of single variable.

Lecturer: Roxana Popescu
Date: October 11

Recitation instructors: George Sparling & Cezar Lupu
Date: October 13


Week 7. Linear Algebra I (video)

Abstract: This will cover problems on topics such as matrices and determinants.

Lecturer: Cezar Lupu
Date: October 18

Recitation instructors: George Sparling & Cezar Lupu
Date: October 20


Week 8. Number Theory I

Abstract: This will cover problems on topics such as arithmetic of numbers, prime numbers and diophantine equations.

Lecturer: Thomas Hales
Date: October 25

Recitation instructor: George Sparling
Date: October 27


Week 9. Number Theory II

Abstract: This will cover problems on topics such as arithmetic functions and quadratic residues.

Lecturer: Thomas Hales
Date: November 1

Recitation instructor: George Sparling
Date: November 3


Week 10. Real Analysis III (video)

Abstract: This will cover problems on topics such as Riemann sums and integrals.

Lecturer: Cezar Lupu
Date: November 8

Special lecture! Generating Functions and Applications

Lecturer: Vlad Matei (University of Wisconsin-Madison)
Date: November 10


Week 11. Linear Algebra II

Abstract: This will cover problems on topics such as vector spaces, linear transformations, characteristic polynomial, eigenvalues  and eigenvectors.

Lecturer: Cezar Lupu
Date: November 15

Recitation instructors: George Sparling & Cezar Lupu
Date: November 17


Week 12. Thanksgiving break!

Abstract: No seminar this week!

Date: November 22 & 24


Week 13. Real Analysis IV (video)

Abstract: This will cover problems on special topics in analysis and beyond.

Lecturer: Cezar Lupu
Date: November 29

Special lecture! Problems with similar ideas in Integral Calculus (video)

Lecturer: Cezar Lupu
Date: December 1


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Putnam’16 squad

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