Workshops - Workshops for Teachers - Competition - Career Panel -  Schedule

Sponsors:

CH- Foundation

Helen-Jones-Foundation

Department of Mathematics and Statistics of TTU,

MAA Texas Tech Student Chapter

SIAM Texas Tech Student Chapter

  Professor Dr. Linda Allen and Assistant Professor Dr. Lih-Ing Roeger (Texas Tech University):

                 Measles, Mumps, and Mathematics

  Assistant Professor Dr. Petros Hajicostas (Texas Tech University): Sister Celine and Sums of Binomial Coefficients

Sister Mary Celine Fasenmyer was born in Pennsylvania in 1906. She joined Sisters of Mercy in 1933 and she got a Ph.D. in Mathematics in 1946 at the University of Michigan.  In her thesis she developed a method for finding recurrence relations for hypergeometric polynomials, and in particular for polynomials involving binomial coefficients. (Binomial coefficients are related to Pascal’s triangle.) Even though she published her work in two papers, the full importance of her work was not realized until 1978 when Doron Zeilberger used her results to prove combinatorial identities. Using her methods and results, Zeilberger and another mathematician, Herbert Wilf, developed a mathematical theory (known today as WZ theory) that allows for extremely elegant proofs of certain classes of  combinatorial identities.

In this presentation, we will examine some elementary ideas behind Sister Celine’s algorithm. We will deal mostly with sums of binomial coefficients.

At the age of 87, in 1994, Sister Celine was invited to attend a discrete mathematics conference in Florida (probably the only one she ever attended). According to Professor Wilf, she said to the mathematicians there: “I want you all to know – I really did that work.” She died in Pennsylvania in 1996.

  Assistant Professor Dr. Arne Ledet (Texas Tech University):  Juggling and Algebra

If we ignore various details (such as making it look good or be funny), juggling can be described by number sequences in a very simple way. This makes it possible to count how many different ways there are to juggle, say, three balls. Also, it can be used to come up with new juggling patterns.

  Assistant Professor Dr. Chris Monico (Texas Tech University):  Factoring Integers to Break Codes

Factoring integers is easy, right? After all, 35 = 5 x 7 -- how hard was that? As a matter of fact it is a very hard problem,even for a computer, if the number is larger (say, 300 digits). Almost every time we buy something from Amazon.com or do anything on the Internet which is encrypted, we are trusting our personal information to the fact that factoring integers is hard. For if someone could factor large integers quickly, they could break RSA encryption, which guards almost all of the secure Internet traffic today!
So what does factoring integers have to do with cryptography at all?It is not so tough to come up with some method of encrypting information which has nothing to do with factoring integers. While this is true, RSA encryption is used to solve a problem which you may not have thought about before. When you are surfing around on Amazon.com, your computer is not directly linked to theirs. Instead, your computer is linked to a computer that's linked to a computer that's linked to a computer ... that's linked to Amazon.com. Any of the computers in between can freely eavesdrop onall of your communications with each other. But when you decide to buy something, you go to an `encrypted page'. In order for this to be reasonable, though, you and Amazon.com must agree on the type (or key) of encryption that you will use. But if an eavesdropper is listening the whole time, won't he or she also know the encryption that you two will use? Imagine this problem very concretely: You say to Amazon.com, ``Let's encrypt our data with method X to communicate securely'' and they reply ``OK''. Well then the eavesdropper in between sees all of this and knows what method you're using. Since he or she has all the same software as you, they can decrypt data with method X as well. It's quite a conundrum. This is precisely the problem that the RSA method (named after its inventors Rivest, Shamir and Adleman) solves. It gives a very clever mathematical computation by which you and your favorite web site can choose your encryption method without the eavesdropper knowing. That is, the eavesdropper still sees all of your communications, but if they want to know exactly what you've said, they must first factor some extremely large integer!
 

  Professor Dr. Lawrence Schovanec (Texas Tech University):Mathematics of Human Body Mechanics

            Since the time of the Renaissance, mathematicians have made fundamental contributions to the understanding of human body structure and its relation to movement.  Rene Descarte and Leonardo da Vinci were two of the first mathematicians to study how skeletal muscles act on bones, using them as levers, to lift weights and produce motion.  Newton's laws and the foundation of classical mechanics set the stage for further studies of human movement.  Today, the combination of mathematics and computing technology is basic to much of the research in the field of biomechanics.

            This workshop will involve activities that illustrate how vector algebra and calculus are used to formulate laws of physics applied to problems in biomechanics.  Particular subjects to be studied, through the use of experiments and calculations, will include moment, torque, levers, kinetics and kinematics, and muscle contraction.

            Workshops for Teachers

  Assistant Professors Dr. Carl Seaquist and Dr. Padmanabhan Seshaiyer (Texas Tech University):

              Calculations across Cultures and History

In this presentation teachers will be given a hands-on opportunity to learn about a variety of ways to calculate including using Napier's bones, Lucas-Genaille rods, slide rules, abacuses (Chinese and Russian), Vedic sutras, and paper and pencil. This variety of ways to calculate has been successfully used with students to connect mathematics, history, and geography.

 Professor Dr. Monty Strauss (Texas Tech University): On Infinity

Large numbers have been of interest throughout the history of civilization. Many interesting things have been "discovered" by the use and misuse and even abuse of infinity. We will talk about some of these.

                                                       Competition

The problems are posed by Dr. Wayne Lewis (Department of Mathematics and Statistics, Texas Tech University). 

The prices are sponsored by the Students Chapters of the MAA and SIAM of Texas Tech University.

Best exam of

Seminole High School: Amanda Riojas

(honorable mention: Lori Flores) 

Spade High School: Shayna Anzaldua

Tahoka High School: Amanda Truelove

(honorable mention: Sarah Blaylock)

Roosevelt High School: Stephanie Overson

(honorable mention: Jessica Farris)

                                                                   Career Panel

                                              On Becoming a Mathematician

    Dr. Delores Ludwig, Director of Cooperative Education  (Office of the Dean of Engineering, Texas Tech University)

                                leads the discussion.

    Dr. Molly Dickens

   Dr. Kathleen Gilliam, lecturer (Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX)

Dr. Kathleen Gilliam completed her Ph.D. in statistics at Texas Tech University in 1998. Since graduating, she has held a research position in the Wind Engineering Research Center at Texas Tech and also teaches statistics to 400 business students each semester in the Department of Mathematics. She has more than 30 publications to her credit, most of them related to the modeling of wind and pressure fields and statistical analysis of wind data. Dr. Gilliam's training in applied mathematics together with her statistical background have provided several advances in signal processing for nonstationary and intermittent processes. More specifically, her related research projects have included: the use of wavelet analysis to detect localized structures in hurricane windfields; locally stationary modeling of wind- and pressure fields; using system identification to analyze overall wind loads; and the application of projection pursuit and proper orthogonal decomposition methods to identify independent flow mechanisms in pressure fields.
   

   Dr. Cindy A. Martin, assistant professor  (Department of Mathematics, McMurry University, Abilene, TX)

I graduated from Texas Tech with a PhD in Applied Mathematics in May 2003. I am now an assistant professor of mathematics at McMurry University in Abilene Texas. I am responsible for teaching all levels of mathematics. The best part of teaching mathematics is the interaction with my students. In my spare time I enjoy reading, playing racquetball, and spending time with my friends.

   Agaytha H. Reed, Manager of Documentation and Quality Assurance

I received my Master of Science degree in mathematics from Texas Tech in August 1992. I currently manage the technical writers and software testers at INCODE, Inc. Every math problem I've ever solved has helped prepare me for the type of disciplined thinking that I need to do my job. When I interview job applicants, I like to find out which math courses they've taken and whether they enjoy math. Needless to say, "I took the minimum required for a degree" and "I hate math!" are not the answers I'm hoping to hear.

9:00-9:30

CHEM49

Welcome and  Introduction

 by  Dr. Jane Winer, Dean of Arts & Sciences, and

                    our Department Head Dr. Lawrence Schovanec

and Registration

9:30-10:45

CHEM49 and CHEM107

9:40-10:30

MATH110

Workshop I for Teachers: Dr. Monty Strauss On Infinity

11:00-11:50

MATH010

MATH011

MATH012

MATH013

MATH014

MATH015

Workshops I for Students

Dr. Linda Allen and Dr. Lih-Ing Roeger: Measles, Mumps, and Mathematics

Dr. Petros Hadjicostas: Sister Celine and Sums of Binomial Coefficients

Dr. Arne Ledet: Juggling and Algebra

Dr. Chris Monico: Factoring Integers to Break Codes

Dr. Lawrence Schovanec: Mathematics of Human Body Mechanics

Dr. Magdalena Toda: 2-D and 3-D Tilings: Our Dream Houses

12:00-1:00

Frazier Pavilion

1:05-1:55

MATH010

MATH011

MATH012

MATH013

MATH015

MATH110

Workshops II for Students

Dr. Linda Allen and Dr. Lih-Ing Roeger: Measles, Mumps, and Mathematics

Dr. Petros Hadjicostas: Sister Celine and Sums of Binomial Coefficients

Dr. Arne Ledet: Juggling and Algebra

Dr. Chris Monico: Factoring Integers to Break Codes

Dr. Magdalena Toda: 2-D and 3-D Tilings: Our Dream Houses

Workshop II for Teachers:

Dr. Carl Seaquist and Dr. Padmanabhan Seshaiyer  Calculations across Cultures and History

2:00-2:45

CHEM49

Career Panel

               On Becoming a Mathematician

                               led by Dr. Delores Ludwig (College of Engineering)

 with Dr. Molly Dickens, Dr. Kathleen Gilliam,  Dr. Cindy Martin, and  Agaytha Reed

2:45 - 3:00

CHEM49