The benefits of involvement in the Math Honors-in-Discipline program include: consideration for an HiD scholarship (decisions for these are made by the Honors College, not by the Math HiD coordinator), the opportunity to take classes as honors enhanced, the opportunity to be involved in other honors enhancement activities (attending seminars, Honors College activities, attending Math conferences, participating in undergraduate research), getting an HiD medallion to wear to graduation, and having your transcript marked "Honors in Discipline" when you graduate.

Mathematics Honors students are encouraged to become active in the ETSU Mathematics Association of America (MAA) chapter. They are also encouraged to participate in the Math Department seminars. Opportunities may also present themselves to attend math meetings at ETSU and nearby universities (such as Appalachian State University, Western Carolina University, and the University of Tennessee).

**Honors-Enhanced Classes**

Honors-enhanced sections of classes carry the section number 088. Honors-enhanced math classes are taught along with the corresponding regular math class (with the exception of Honors Calculus 1 [MATH 1910-088]). In order to get a math class approved as honors-enhanced, a list of proposed enhancement experiences must be submit in writing to the Mathematics Honors-in-Discipline Coordinator by the end of the first week of class. The honors enhancement proposal must include a cover sheet which is available online. When approved, the student drops the regular math class, an honors-enhanced section (numbered 088) is created, and the student adds the honors section (which requires a permit that the math executive aid will create when the 088 section is created). The section must be created by the day of "Late Registration/Add with Departmental Permit only" (which is sometime during the second week of classes - it varies from term to term). Therefore you must act fast in preparing your proposal. An example of an honors enhancement proposal is available here.

* Every honors-enhanced section will include a written report and oral presentation! *The presentation can be done in class, in the departmental seminar, at a professional
meeting, or in the end-of-the-semester SAMHIDD seminar.

The following "enrichment experiences" are examples of possible ways to make a course honors-enhanced. These examples are in large part due to the original Mathematics Honors Coordinator, Jay Boland.

**Calculus 1 (MATH 1910)**

This class is offered in the fall semester of each year. It is designed for the honors
scholars, but is also open to math H-i-D students (with permission).**Calculus 2 (MATH 1920)**

Details coming soon.**Linear Algebra (MATH 2010)**

Details coming soon.**Probability and Statistics - Calculus Based (MATH 2050)**

Details coming soon.**Calculus 3 (MATH 2110)**

Details coming soon.**Differential Equations (MATH 2120)**

Develop models, including formal write-up, class presentation, and world wide web
display for

- Rate of growth of populations (exponential model using linear regression and a differential equation).
- Flow of water from a cylinder (square root model).
- Growth of sunflower plants (logistic model).
- Harvesting of trees (equilibrium solutions of an autonomous differential equation).
- Analyzing temperature (sinusoidal model).
- Determination of amount of solute in two or more containers (systems of first order linear differential equations using eigenvalues).
- Predator-prey model (system of first order non-linear differential equations using PC-Matlab or Maple software).

**Mathematical Reasoning (MATH 2800)**Study of a topic related to logic and proof techniques, with a written report and
presentation, for

- Cantor and cardinality.
- Ordinal numbers.
- Some of Godel's work on undecidability.
- Russel and Whitehead's work and Principia Mathematica.
- Frege's work on the foundations of arithmetic.
- Peano's axioms of arithmetic.
- Dedekind's ideas of "cuts" of the real line and completeness.
- Hilbert and the foundations of geometry.
- Cauchy's introduction of rigor in analysis.
- The four color theorem and what "proof" means.
- The classification of finite simple groups and how the proof of that came about.

Students can concentrate on the historical component or read original papers. There
are several popular level books on these topics and much of the original work is translated
and readily available, some of it even free on the internet. A student may present
a course lecture by introducing one of the topics, presenting it to the class, and
discussing the importance of the topic in contemporary mathematics research. A student
can also pick one of the main topics from the course (i.e., equivalence relations
or proof techniques), find a current research paper dealing with that topic and present
the main points of the paper to the class in a 20-25 minute presentation.**History of Math (MATH 3040)**

Details coming soon.**Statistical Modeling (MATH 3050)**

Details coming soon.**Elementary Number Theory (MATH 3120)**

- Choose a modern application of number theory (such as cryptography) and prepare a 2-3 page paper discussing the application.
- Investigate a topic not covered in the class and prepare a lecture (15-20 minutes) which is to be presented in class.
- Write a 2-3 page historical discussion of a central topic in number theory.

**Applied Combinatorics and Problem Solving (MATH 3340)**

Details coming soon.**Mathematical Statistics 1 (MATH 4047)**

- Solve problems at a higher degree of difficulty than other non-honors students.
- Become familiar with probability distributions not normally covered in class. Also become familiar with families and systems of distributions. The SU and SB Johnson distributions, Tukey's lambda, the four parameter Lambda distribution, the Weibull, Gamma, and Extreme Value distributions are some examples. The study can include theoretical aspects, careful analysis of the shape in relation to the parameters, simulations, applications, etc. Write a 2-3 page paper detailing the distributions studied.
- Reading (and eventually working on) applications of probability in the real world.
- Get acquainted with classical probability topics or problems not covered in the course. Give a presentation in class on the topic.

**Introduction to Modern Algebra (MATH 4127)**

- Investigate the applications of dihedral groups in molecular modeling. Write a 2-3 page paper summeraizing your findings.
- Explore the role of transformation groups in the study of geometry. Describe the group structures of both Euclidean motions and similarity transformations in detail and include a derivation of the equations for these transformations.
- Write a descriptive analysis of the differences between the concepts of group, ring, field, and module. View this as an explanation for fellow students who may not understand the concepts. Include examples and illustrations of each of your main points. Your analysis should consist of at least 2-3 pages.
- Read a book on the history of algebra (group theory, symmetry, simple groups, algebraic solvability), prepare a written report and a PowerPoint presentation to be given in class or in the math department seminar.

**Analysis 1 (MATH 4217)**

- Student must select a current research paper related to real analysis and give a report on that paper either at a student seminar, at the math department colloquium, or in class.
- Read a book on the history of analysis (a biography of a key figure, Newton and Leibniz's calculus war, the rigorous revolution of the 19th century), prepare a written report and a PowerPoint presentation to be given in class or in the math department seminar.

**Analysis 2 (MATH 4227)**

- Investigate applications of Riemann-Stieltjes integration.
- Investigate the mathematics behind generalizations of Riemann integration (such as Lebesgue integration).
- Explore the historical setting which necessitated the development of generalizations to the Riemann integral (such as the Lebesgue integral).

**Complex Variables (MATH 4337)**

- Use a software package (such as F(z), Mathematica, Maple, or Matlab) to geometrically explore some topics from the class. Present the results of these explorations in class.
- Study solutions to various applied problems which involve complex variables (such as partial differential equations or conformal mapping as applied to aerodynamics). Present the results to the class.

**Combinatorics and Applied Graph Theory 1 and 2 (MATH 4340 and MATH 4350)**

- Chemical graph theory: DNA is a chain consisting of bases, where each base is one of four possible chemicals. The sequence of bases encodes certain genetic information. In particular, it determines long chains of amino acids which are known as proteins. How long does a part of a DNA chain have to be for there to be enough possible sequences to encode 20 different amino acids? Numerous projects from this topic can be developed. In fact, there are research journals devoted entirely to combinatorial chemistry and this field is currently one of the "hottest" fields of research.
- Scheduling: A basketball team plays 30 games in 20 days playing at least one game every day. Show that there must be a period of consecutive days during which the team plays exactly 9 games. Is there necessarily a period of consecutive days when exactly 10 games are played? From problems like this, enough expertise can be developed to design more complex schedules.
- Graph models: In a city without one-way streets, a math professor drives to school, which is 8 blocks west and 5 blocks north of his house. In how many ways can he drive to school without ever repeating his entire route if he always avoids a dangerous intersection 2 blocks west and 2 blocks north of his house? In how many ways can he avoid two dangerous intersections: one 2 blocks west and 2 blocks north and the other 3 blocks west and 2 blocks north? From problems like this, the student can model traffic flow in a major city or create the best design for a gas pipeline.