# Off on a Tangent 19.02

Since registration for spring 2021 classes starts soon, we thought you might want to see some details of the upper-level mathematics classes that will be offered.

Math 280: Bridge to Higher Mathematics is designed to help students transition from computational mathematics to problem solving, generalization and abstraction, and writing solutions clearly.  Course topics may include functions and sets, recursion, induction, counting techniques, equivalence relations, an introduction to group theory, and an introduction to real analysis.  The course will be taught via inquiry-based learning and you will work with other students to solve problems together.

MATH 311: Statistical Methods. In this first-half-semester course we will explore statistical inference for one and two variables, starting with simulation-based approaches and then transitioning to traditional theory-based techniques all while aiming to develop a deep conceptual understanding of inferential statistics. Throughout we will explore real research studies through active-learning. This course has the same content and learning objectives as Math 210, but the material is covered in half the time. So it is designed for students who have a significant prior experience with statistics (e.g., high school statistics course) or calculus. (Students cannot receive credit for both Math 210 and Math 311.)

MATH 312: Applied Statistical Models picks up where MATH 311 (or MATH 210) leaves off. In this second-half-semester course we take a deeper look at sources of variation in data and use statistical models to predict values of response variables. These models will now allow for the inclusion of multiple explanatory variables (categorical, quantitative, or a mix), and not just a single explanatory variable as we use in MATH 311. We will again aim at developing a deep conceptual understanding of statistics. Students will also carry out a research project at the end of the semester.

Math 362: Mathematical Statistics. If you enjoyed Math 365 and/or are thinking of pursuing an interest in probability, statistics, or actuarial sciences, consider taking Math 362 this Spring.  We will start the course with the Central Limit Theorem and other results involving long term behavior of random processes.  We will see how these results inform estimation and hypothesis testing in statistics. The class will be an upper-level math course but we will get our hands dirty with a couple of real-world data sets.

Math 360: Combinatorics and Graph Theory. I encourage you to think about taking Combinatorics and Graph Theory this spring.  Both of these fields provide lots of examples that are both easy to understand and filled with complexity.  It is a good setting for practicing your mathematical thinking and proof writing skills.  We will practice proof by induction, proof of bijections, combinatorial proofs, and proofs using the pigeonhole principle.  If practicing math skills isn’t enough motivation, take the course to learn to count cards and evaluate your odds in games of chance.

MATH 370. Advanced Differential Equations picks up where we set differential equations aside in Math 232.  We’ll start by looking at series solutions for solving linear ODEs, a technique that is flexible and broadly applicable.  Then we’ll move into work on partial differential equations.  We’ll do some theoretical and some applied work on the PDEs including separation of variables and Green’s functions.  If there is interest, we’ll also do an introduction to numerical solutions to PDEs via the finite element method.

### Fall social(ly distanced)

Despite having to remain socially distant, we still managed to hold our annual fall social with ice cream treats and some fun games. Below are two pictures from this year’s event and one from a few years ago. Can you tell which is which?

### Problem of the Fortnight

A long hallway has 20,000 LED lights.  Each is operated by a switch that turns the LED light either red or green.  As coincidence would have it, 20,000 people form a line at one end of the hallway (six feet apart and wearing masks, of course).  Initially all the lights are green.  The first person walks through the hallway and turns each light red.  The second person walks through the hallway and hits the switch on every second light, thereby turning all the even-numbered LEDs green.  The third person walks through the hallway and hits the switch on every third LED, turning some red and others green.  The fourth person hits the switch on every fourth LED, and so on.

Which LEDs are red after the 20,000th person has passed through the hallway? You can find the solution here. (But don’t peek unless you’ve got an answer to check!)

### Midstates Consortium’s Undergraduate Research Symposia

If you’ve completed research recently, you may be able to present your results at one of the two Midstates Consortium’s Undergraduate Research Symposia online hosted at University of Chicago and Washington University in St. Louis.

Students who have done research in Psychology, Biology, Chemistry, Physics, Engineering, Math, Computer Science, Neuroscience, and related fields are encouraged to apply.