Chattanooga Math Circle
About Chattanooga Math Circle
There is a correlation between problem solving and the learning process of mathematics. Strong problem solving skills have considerable effect in transforming a mathematics enthusiast into an exceptional researcher. Following the traditions of Russian and Eastern European math circles, Chattanooga Math Circle is a creative enrichment program geared toward gifted middle and high school students in grades 710. Its objectives are:

to provide an enriching and stimulating environment that encourages further involvement from students already interested in mathematics;

to promote mathematics to a wider audience and explain its impact and relevance for society;

to develop the mathematical background of students; and

to guide students towards promising careers in science, technology, engineering, and mathematics (STEM) disciplines.
The Math Circle includes the following major components:

a series of mathematically intensive, expository seminars on a variety of pure, applied and computational mathematics topics designed to challenge top Chattanooga students;

special guest lectures that show students some of the ways mathematicians approach problems;

collaborative problem solving activities that focus on complex problems and advanced problem solving techniques; and

workshops on American Mathematics Competitions (AMC) 8 and 10/12 B.
The Math Circle focuses on topics outside of what is typically covered in a middle and high school setting but accessible to the mathematically inclined students. These are as varied as advanced Euclidean geometry, elementary number theory, fractals, combinatorics, graph theory, probability, statistics, game theory, and logic. Under the guidance and instruction of mathematics faculty and supported by talented undergraduate mathematics majors, students will have the opportunity to learn and explore a variety of effective problem solving strategies. Students can expect to be supported in an environment with events and activities that help them learn quickly and push outside their comfort zone, to grow their skills and gain valuable insights into various mathematical problems, and to have a lot of fun learning beautiful and useful mathematics.
Fall 2018 Schedule
The format is that of one and a half hours meeting, from 5:00 PM to 6:15 PM on Thursdays. The Math Circle will meet in Room 232 of the Engineering, Mathematics, and Computer Science (EMCS) Building starting September 13th and continuing until November 22nd. After hours parking is free in Lot 10. Parents are welcome to use the UTC Library while their children are participating in the Math Circle. The latest books and magazines are in the common area of the first floor of the UTC Library.
Date 
Title 
Speaker(s) 
9/13 
Applications of Congruences: Check Digits 
Andrew Ledoan 
9/27 
Pauli Matrices and Commutation 
Roger Nichols 
10/18 
Sum of Squares 
Andrew Ledoan 
11/1 
Probability 
Andrew Ledoan 
11/15 

Lakmali Weerasena 
11/22 
Thanksgiving Day – No Session 

Math Circle Instructors
The Math Circle instructors are faculty members and graduate and undergraduate students from The University of Tennessee at Chattanoooga (UTC):

Dr. Andrew Ledoan, UTC, Director

Dr. Roger Nichols, UTC, CoDirector

Dr. Cuilan (Lani) Gao, UTC, CoDirector

Dr. Lakmali Weerasena, UTC

Mr. Matthew Villanueva, UTC

Ms. Rhionna Sims, UTC
Upcoming Mathematics Competitions
The AMC is a series of national mathematical competitions of increasing difficulty organized annually by the Mathematical Association of America. Participants are middle school and high school students. According to AMC, the competitions are intended for everyone from the average student at a typical school who enjoys mathematics to the very best student at the most special school. The AMC starts with AMC 8 and AMC 10/12, continues with the American Invitational Mathematics Examination (AIME) for students who qualify, and finishes with the United States of America Mathematical Olympiad (USAMO). The top participants in the USAMO are invited to take part in the Mathematical Olympiad Summer Program (MOSP), where a US team for the International Olympiad is selected.
The dates for the upcoming AMC contests are:

AMC 8 — Tuesday, November 14, 2017

25 multiple choice questions in 40 minutes

AMC 8 is for grades 6, 7, and 8


AMC 10/12 A — Tuesday, February 7, 2018

AMC 10/12 B — Wednesday, February 15, 2018

25 multiple choice questions in 75 minutes

AMC 10 is for grades 910 (top 2.5% nationally qualify for the AIME)
 AMC 12 is for grades 1112 (top 5% nationally qualify for the AIME)

Typically, students take AMC 10/12 B at their schools. However, if their school is not offering the test, they can now take it at UTC. For banks of AMC problems, visit the Art of Problem Solving’s AoPSolving Wiki website.
AIME

10,000 students are invited (March)

15 questions in 3 hours, each answer is an integer number 0999
USAMO

500 students are invited (April)

6 essay/proof questions in 2 days (9 hours)

12 students are invited to the award ceremony in Washington, DC
MOSP

50 students are invited: IMO team (6 students), 2 alternates, 17 younger top students, 25 top

3 to 4 weeks (intensive)
IMO

6 students represent the USA

6 essay/proof questions in 2 days (9 hours)
Old Math Circle Sessions
Date 
Title 
Speaker(s) 
9/15 
Linear Difference Equations and Applications, Part I, Worksheet Solutions 
Roger Nichols 
9/29 
Oh the Places You Will Go: Becoming WellEuled Mathematicians 
Debra Mimbs & Laura Singletary (Lee University) 
10/20 
Explicit Methods for Solving Diophantine Equations, Part I, Worksheet Solutions 
Andrew Ledoan 
10/27 
Explicit Methods for Solving Diophantine Equations, Part II, Worksheet Solutions 
Andrew Ledoan 
11/10 
Mathematical Billiards: Playing Pool with Geometry and Topology 
Jason Schmurr (Dalton State) 
11/17 
Adventures in Data Science, Worksheet Solutions 
Cuilan (Lani) Gao 
12/8 
Review Session for AMC 10/12 B 
Roger Nichols & Andrew Ledoan 
Date 
Title 
Speaker(s) 
2/9 
Gauss’s Congruence Relation, Worksheet Solutions 
Andrew Ledoan 
2/23 
Analytic Inequalities, Worksheet Solutions 
Roger Nichols 
3/9 
Fractal Geometry, Worksheet Solutions 
Billy Jackson (UTC) 
3/29 
Data Analysis, Worksheet Solutions 
Cuilan (Lani) Gao 
4/13 
The Pigeonhole Principle, Presentation Slides, Pamphlet 
Heunggi Park (Covenant College) 
4/27 
Domination in Graphs, Worksheet 
Lucas Van der Merwe (UTC) 
Date 
Title 
Speaker(s) 
9/7 
Pythagorean Triangles 
Andrew Ledoan 
9/14 
Majorization and Muirhead’s Theorem 
Roger Nichols 
9/21 
Exploring a Mathematical Magic Trick: Liar’s Bingo 
Sarah TrebatLeder (Art of Problem Solving) 
9/28 
AMC 8 and AMC 10 Workshops 
Shannon Hyder, Rhionna Sims, Roger Nichols, Andrew Ledoan 
10/5 
Difference Equations and Their Applications to Population Dynamics 
Jin Wang (UTC) 
10/12 
Hamilton County Fall Break (No session) 

10/19 
Polygon Differencing Games 
Philip Yasskin (Texas A&M University) 
10/26 
AMC 8 and AMC 10 Workshops 

11/2 
Prime Numbers 
Andrew Ledoan 
11/9 
Understanding the Law of Large Numbers and the Central Limit Theorem by Looking at Color Distribution of M&M Candies 
Cuilan (Lani) Gao 
11/14 


11/16 
Walking On and Coloring Graphs 
Ben Webb (Brigham Young University) 
11/23 
Thanksgiving Holiday (No session) 

11/30 
Mathematical Induction 
Roger Nichols 
12/7 
AMC 10 Workshop 
Shannon Hyder, Rhionna Sims, Roger Nichols, and Andrew Ledoan 
12/14 
Who Wants to Be a Mathematician? (Quiz competition) 
Shannon Hyder, Rhionna Sims, Roger Nichols, and Andrew Ledoan 
Date 
Title 
Speaker(s) 
1/18 
Aspects of Discrete Mathematics I 
Andrew Ledoan 
1/25 
AMC 10/12 Workshop 
Shannon Hyder, Rhionna Sims, Matthew Villanueva, Roger Nichols, and Andrew Ledoan 
2/1 
Aspects of Discrete Mathematics II 
Roger Nichols 
2/8 
AMC 10/12 Workshop 
Shannon Hyder, Rhionna Sims, Matthew Villanueva, Roger Nichols, and Andrew Ledoan 
2/15 
AMC 10/12 Competitions 
No Session 
2/22 
Some Topics on Unusual Geometry 
Boris Belinskiy (UTC) 
3/1 
An Introduction to Cryptography and Modular Arithmetic 
Matthew Villanueva (UTC) 
3/8 
Some Topics in Abstract Mathematics 
Matthew Villanueva (UTC) 
3/22 
Misleading Statistics 
Aniekan Abiefung (UTC) 
3/29 
Visualizing Data Using Graphs–Example of the Winter Olympics Medals Data 
Lani Gao 
4/5 
Hamilton County Spring Break 
No Session 
4/12 
Rocket Science Really is Rocket Science! 
Paul Crawford (Marshall Space Flight Center) 
4/19 
Can You Spot It?! 
Philip DeOrsey (Westfield State University) 
4/26 
Mathematical Programming 
Lakmali Weerasena (UTC) 