2nd Emmy Noether High School Mathematics Day  
Texas Tech University, Department of Mathematics and Statistics  
May 4th 2004  
Thank you very much
to everybody who helped to make this great day happen!
to our sponsors the Department of Mathematics and Statistics, the CH Foundation, the
Helen Jones Foundation, the Local MAA Student Chapter, and the Local SIAM Student Chapter
to our panelists Delores Ludwig (chair), Molly Dickens, Kathleen Gilliam, Cindy Martin ,
and Agaytha Reed
to our volunteers Theresa Busse, Rachel Cline, Amy Drew, Keith Emmert, Sheyleah Harris, Daniel Holder, Lourdes Juan, Dustin Love, Kiyomi Kaskela, Eric Murphy, Jessica Parras, Victor, Patrangenaru, Shan Sun, Edward Swim, Brock Williams, and Lina Williams
to our workshop presenters, and organizing committee
to our department and, in particular, Margaret Plunket for daily support
and of course
to the 145 students and 15 instructors from
Cotton Center High School, Estacado High School, Levelland High School, Littlefield High School, Roosevelt High School, Seminole High School, Spade High School, Tahoka High School, and Wilson High School.
Workshops  Workshops for Teachers  Competition  Career Panel  Schedule
Sponsors:


CH Foundation HelenJonesFoundation Department of Mathematics and Statistics of TTU, MAA Texas Tech Student Chapter SIAM Texas Tech Student Chapter

Workshops for Students

Professor Dr. Linda Allen and Assistant Professor Dr. LihIng 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!

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.

Assistant Professor
Dr. Magdalena Toda (Texas Tech University): 2D and 3D Tilings: Our Dream Houses We will construct various tilings of surfaces and spaces. We will find what it takes to construct regular and semiregular tilings.Students will have to construct and name some tilings themselves, based on two criteria: types of regular polygons to be used, and nodal configuration(s). Each student will be encouraged to come up with her favorite floor/ceiling/wall tiling: creativity is a must. Finally, we will explore several three dimensional tilings which appear in nature (crystalography, architecture, biology). A flight simulator in the (tiled!) hyperbolic space will conclude our workshop.

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 handson opportunity to learn about a variety of ways to calculate including using Napier's bones, LucasGenaille 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. 
Our winners are:
9th Grade: Amanda Truelove from Tahoka High School  Best School in School Division 1A and 2A: Wilson High School 
10th Grade: Dayton Castro from Levelland High School  Best School in School Division 3A and 4A: Seminole High School 
11th Grade: Kylie Bates from Levelland High School  
12th Grade: Amanda Riojas from Seminole High School  
Best exam of 

Cotton Center High School: Kami Payne 
Seminole High School: Amanda Riojas (honorable mention: Lori Flores) 
Estacado High School: Ashley Bural 
Spade High School: Shayna Anzaldua 
Levelland High School: Kylie Bates 
Tahoka High School: Amanda Truelove (honorable mention: Sarah Blaylock) 
Littlefield High School: Aimee Marquez  Wilson High School: Lorena Gonzale 
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.

Panelists: 
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 (Incode Inc., Lubbock,
TX)
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. 
Schedule  
9:009:30 CHEM49 
Welcome and Introduction by Dr. Jane Winer, Dean of Arts & Sciences, and our Department Head Dr. Lawrence Schovanec
and Registration

9:3010:45 CHEM49 and CHEM107
9:4010:30 MATH110 
Student
Competition
Workshop I for Teachers: Dr. Monty Strauss On Infinity

11:0011:50
MATH010
MATH011
MATH012
MATH013
MATH014
MATH015 
Workshops I for Students Dr. Linda Allen and Dr. LihIng 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: 2D and 3D Tilings: Our Dream Houses

12:001:00 Frazier Pavilion

lunch 
1:051:55
MATH010
MATH011
MATH012
MATH013
MATH015
MATH110 
Workshops II for Students Dr. Linda Allen and Dr. LihIng 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: 2D and 3D Tilings: Our Dream Houses
Workshop II for Teachers: Dr. Carl Seaquist and Dr. Padmanabhan Seshaiyer Calculations across Cultures and History

2:002:45 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 
Awards, Evaluations, and Closing 