Department of Mathematics of the Pennsylvania State University runs a yearly semester-long intensive program for undergraduate students seriously interested in pursuing a career in mathematical sciences. The *Mathematics Advanced Study Semesters* (MASS) program started in the Fall of 1996 and is held during the Fall semester of each year.

The principal part of the program consists of three courses chosen from major areas in Algebra / Number Theory, Analysis, and Geometry / Topology, specially designed and offered exclusively to MASS participants. Each course features three lectures per week, a weekly recitation session conducted by a MASS teaching assistant, weekly homework assignments, a written midterm exam and an oral final exam.

In the fall of 2014, the students will be able to choose one of the following two options:

the three courses or two of the three courses and a research project.

The program also includes a weekly interdisciplinary seminar that helps to unify all other activities and MASS Colloquium, a weekly lecture series by visiting and resident mathematicians.

## Courses

The following courses will be offered in the Fall of 2014:

*Finite Fields and Applications*

Instructor: Gary Mullen, Professor of Mathematics

Teaching Assistant: Daniel Droz

113 McAllister Building, MWRF 10:10 - 11:00 a.m.*Affine and Projective Geometries*

Instructor: Yakov Pesin, Distinguished Professor of Mathematics

Teaching Assistant: Alena Erchenko

113 McAllister Building, MTWF 1:25 - 2:15 p.m.*An Introduction to Dynamical Systems*

Instructor: Victoria Sadovskaya, Associate Professor of Mathematics

Teaching Assistant: Kurt Vinhage

113 McAllister Building, MWRF 11:15 a.m. - 12:05 p.m.*MASS Seminar*

Instructor: Victoria Sadovskaya, Associate Professor of Mathematics, Interim MASS Director

113 McAllister Building, Tuesday 10:10 a.m. - 12:05 p.m.*MASS Colloquium*

Instructor: Multiple invited speakers

114 McAllister Building, Thursday 1:25 - 2:25 p.m.

## Course Outline

**Math 497A - Honors MASS Algebra**

**Finite Fields and Applications**

Instructor: Gary Mullen, Professor of Mathematics

TA: Daniel Droz

113 McAllister Building, MWRF 10:10 - 11:00 a.m.

*Description:* This course will consist of an introduction to the theory of finite fields. We will also discuss some of the many practical applications of finite fields. These applications will include algebraic coding theory for the error-free transmission of information and cryptology for the secure transmission of information. Finite fields are also of great use in the construction of various kinds of combinatorial designs.

*Reading:* G. Mullen and C. Mummert: Finite Fields and Applications. ISBN: 978-0-8218-4418-2.

**Math 497B - Honors MASS Analysis**

**An Introduction to Dynamical Systems**

Instructor: Victoria Sadovskaya, Associate Professor of Mathematics

TA: Kurt Vinhage

113 McAllister Building, MWRF 11:15 a.m. - 12:05 p.m

*Description:* The theory of dynamical systems is a modern branch of mathematics. Its main objective is to analyze long-term behavior of systems that evolve over time. In this course, we will introduce the fundamental concepts and tools of dynamics and discuss an array of examples with gradual increase in complexity. The topics will include contractions, linear maps, differential equations, recurrence, equidistribution, hyperbolic systems, symbolic systems and coding, fractals, entropy, and chaos.

*Reading:* B. Hasselblatt and A. Katok: A First Course in Dynamics with Panorama of Recent Developments. ISBN: 978-0-5215-8750-1.

**Math 497C - Honors MASS Geometry**

**Affine and Projective Geometries**

Instructor: Yakov Pesin, Distinguished Professor of Mathematics

TA: Alena Erchenko

113 McAllister Building, MTWF 1:25 - 2:15 p.m.

*Description:* This course is an introduction to Geometry and its goal is to describe Geometry following Felix Klein’s Erlangen program, that is as the action of the group of isometries. The emphasis is on Affine, Projective and non-Eucleadian (Lobachevsky-Poincare hyperbolic) geometries.

*Reading:* A. B. Sossinsky: Geometries. ISBN: 978-0-8218-7571-1.

## Calendar of Events

Arrival Day | August 24 |

MASS Orientation | August 25, 9:30 a.m. |

Classes Begin | August 25 |

Labor Day — No Classes | September 1 |

Midterm Exams | October 6, 7, 8 |

Thanksgiving Holiday — No Classes | November 23-29 |

Classes End | December 5 |

Study Days | December 6-11 |

Final Exams | December 12, 15, 17 |

MASS Graduation Ceremony | December 18, 10 a.m. |

## Enrollment

Participants are selected from applicants who will be juniors or seniors in the following academic year (sophomores may be admitted in some cases). All participants are expected to have demonstrated a sustained interest in mathematics and a high level of mathematical ability and to have mastered basic techniques of mathematical proof. The expected background includes a full calculus sequence, basic linear algebra, a transition course with proofs (such as discrete mathematics) and advanced calculus or basic real analysis. The search for participants is nationwide. International applications are invited as well. Each participant is selected based on academic record, two recommendation letters from faculty, and an essay (international applicants should demonstrate their mastery of English).

Candidates should submit:

- Application Form
- Transcript
- Record of Mathematics Courses
- A short essay describing their interest in mathematics
- Two letters of recommendation
- Financial disclosure form
- Transfer Protocol form

Application materials may be retrieved off the web, or requested by mail, fax, or e-mail.

Applications should be submitted through MathPrograms.org, ID: PSUMASS or sent by mail, fax, or e-mail to

107 McAllister Building

Department of Mathematics

Penn State University

University Park, PA 16802

(814) 863-8730 / Fax:(814) 865-3735

E-mail: mass@math.psu.edu

The deadline for MASS applications is **Friday, April 4, 2014.**

## Financial Arrangements

Successful applicants currently enrolled in U.S. colleges and universities will be awarded the Penn State MASS Fellowship which reduces the tuition to the in-state level. Best efforts will be made not to increase their out of pocked expenses. See the Financial Information for more details.

## Housing

All participants not enrolled at Penn State will be provided an opportunity to live in one of the residence halls on campus.

## Credits

The program elements total 16 credits, all of which are recognized by Penn State as honors credits and are transferable to participants' home universities. Students will also receive a certificate from the MASS Program at Penn State. Additional recognition may be provided through prizes for outstanding performance and for best projects.

## Administration

The overall supervision of the MASS program is provided by the Scientific Advisory Board which includes senior members of Penn State's mathematics faculty, and several outstanding mathematicians from other institutions.

The program is managed by the Director Sergei Tabachnikov.

Stephanie Zerby is the Administrative Assistant for the MASS program.

Participants are chosen by the *Selection Committee* headed by a member of the Scientific Advisory Board.