Current Courses

Spring 2020

MTH 110 Introduction to Statistics I (no Computer Lab) -- A data-oriented, applied introduction to statistics. Topics include descriptive statistics, data distributions, random sampling, relationships, confidence intervals, and hypothesis testing. Statistical software will be used throughout this course.

Summer 2020

MTH 145 Calculus I (Online) -- A study of differential and integral calculus of one variable and applications.

Teaching Philosophy

“The teacher can open the door, but you must enter by yourself.” -- Ancient Proverb.

I believe that students can learning anything provided they have enough interest, enough determination, and enough time. Of course, the amount of each that is required depends on the individual learner and the desired topic. Unfortunately(?), we have yet to reach the age of directly uploadable knowledge and skills, á la the Matrix. Thus, real learning still takes hard work and perserverance through difficulties and failures. In fact, we learn the most from our mistakes, as long as we're willing to analyze what went wrong and how to fix it.

As the proverb suggests, educators can do their best to set you up for success, to lead you to the right sorts of failures and perspectives that drive new insight, to create scenarios and environments ripe for a-ha moments, but you (the learner) must make the new mental connections yourself. I hope that my excitement for mathematics (and learning in general) is contagious and that I can inspire you to continually challenge yourself and persevere to new understanding for the rest of your life.

Some Recent Senior Projects

Here are some fun examples of senior projects (MTH 495) that I have advised in recent years. Some of these actually turned into publications in peer-reviewed journals!

Analysis of the Best Strategy for Prime Climb
Claire Hiwiller, Fall 2019

Prime Climb is a beautiful mathematical game created by Katherine Cook and Daniel Finkel. In it, players roll two 10-sided dice and apply the resulting numbers one at a time to your current position(s) using the arithmetic operations +, −, ×, ÷. The goal is to get both of your pawns to position 101 before the other players do. If you decide on a strategy ahead of time, then you can model this game using a Markov chain and compute the expected number of turns to complete the game. This gives you a metric by which to compare different strategies as well. Which strategy is the best?

Solving nxn Boards Using Minimal Clues
Julia Richey, Fall 2019

Cross Set is a puzzle game, with some similarity to Sudoku, which was developed by Cuveet Story and released on the Steam gaming platform. To complete each level, you must take the clues that are given (which numbers could possibly appear in each cell) and successfully complete the board to create a Latin square (i.e. each number appears exactly once in each row and column). What is the minimum number of clues required to force the puzzle to have a unique solution?

A Twist on the Two Digits Game
Nina Scrimale, Fall 2017

Two Digits was developed by Cleverweek and was released on the Steam platform in 2015. To complete each level in the game you must find two disjoint subsets of integers that add up to the same total. The standard levels are played with nine distinct numbers, each ranging from 1 to 100. Generalizing, we could be given any fixed number (≥3) of distinct integers. If we'd like to guarantee that there exists a solution, regardless of the choice of integers, then to what domain of values must we restrict our choices?

A 9-by-9 Numbrix puzzle

Numbrix Puzzles
Mary Grace Hanson, Spring 2017

Numbrix puzzles were created by Marilyn vos Savant and (the 9×9 variety) have been regularly featured in Parade Magazine. If we allow puzzles of any size m×n, what is the minimum number of clues that must be given (for each size) for the puzzle to be solvable?

The Top Spin Puzzle

Analyzing the Oval Track Group
Sara Randall, Fall 2016

The Top Spin puzzle was invented by Binary Arts (now Think Fun) in 1989. It has since been (mathematically) generalized to Oval Track puzzles by allowing the number of tiles and the size of the turntable to vary. Now, what if you were to take a hammer to this puzzle and knock all of the tiles out? If you wanted the puzzle to remain solvable, would it matter how you return them to the track?

A generically labeled Fano Plane

The Magic Fano Plane
Ben Miesner, Fall 2013

Similar to the famous Magic Squares, you could imagine placing numbers at the vertices of a Fano plane and summing along each line (including the circle). Is it possible for all of those sums to be the same while having all of the individual numbers different? What if you are allowed to use modular arithmetic instead?

Past Courses

Fall 2010

  • MTH 146 Calculus II -- A study of differential and integral calculus of one and several variables and applications. Differential equations and their solutions.
  • MTH 341 Abstract Algebra -- Introduction to group theory. Cyclic, Abelian, symmetric and product groups. Subgroups, equivalence relations, homomorphisms.
  • MTH 341 Abstract Algebra

Spring 2011

  • MTH 145 Calculus I -- A study of differential and integral calculus of one variable and applications.
  • MTH 145 Calculus I

Summer 2011

  • MTH 145 Calculus I
  • MTH 146 Calculus II

Fall 2011

  • MTH 145 Calculus I
  • MTH 245 Calculus III -- Multi-variate calculus with vectors. Line integrals and Green's theorem.
  • MTH 341 Abstract Algebra

Spring 2012

  • MTH 245 Calculus III
  • MTH 370 Intermediate Problem Solving -- A working introduction to general heuristic reasoning (including specialization, generalization, analogy and induction) useful in solving mathematical problems.

Fall 2012

  • MTH 261 Linear Algebra -- Systems of linear equations, matrix algebra, vectors and vector spaces, linear transformations, inner product spaces, determinants, characteristic values and vectors.
  • MTH 261 Linear Algebra
  • MTH 341 Abstract Algebra

Spring 2013

  • MTH 120 Mathematics for Business Majors -- This course includes the following topics: exponential functions and models, mathematics of finance, linear systems and matrices, linear programming, derivatives. There is particular emphasis on applied problems.
  • MTH 120 Mathematics for Business Majors
  • MTH 131 Discrete Mathematics (Now MTH 260) -- This course covers the fundamental mathematical principles relevant to computer science, applied mathematics, and engineering. Topics included are propositional logic, predicate logic, proof techniques, (with an emphasis on mathematical induction), bascis of counting and discrete probability.

Fall 2013

  • MTH 261 Linear Algebra
  • MTH 261 Linear Algebra
  • MTH 341 Abstract Algebra

J-Mester 2014

  • MTH 145 Calculus I (Online)

Spring 2014

  • MTH 104 Mathematics for Decision Making -- We all need to make decisions. As citizens, we need to sift through the mountain of (often misleading) data that is constantly being thrown our way by advertisers, the media, politicians, etc. As professionals, we may need to make decisions using data from such diverse areas as economics, social policy, health care, the military, or the environment. In any role, we need to know how data can be turned into useful information. This course covers mathematics used to analyze data in order to make good, informed decisions. Major topics include informal logic, data interpretations, basic probability, introductory statistics, and economics.
  • MTH 146 Calculus II
  • MTH 146 Calculus II

Summer 2014

  • MTH 145 Calculus I (Online)

Fall 2014

  • MTH 120 Mathematics for Business Majors
  • MTH 261 Linear Algebra
  • MTH 341 Abstract Algebra

J-Mester 2015

  • MTH 145 Calculus I (Online)

Spring 2015

  • MTH 104 Mathematics for Decision Making
  • MTH 245 Calculus III

Summer 2015

  • MTH 145 Calculus I (Online)

Fall 2015

  • MTH 122 Brief Calculus -- Elementary functions, exponential and logarithmic functions, continuity, derivatives, max-min methods and applications. Primarily for students in economics and accounting.
  • MTH 261 Linear Algebra
  • MTH 341 Abstract Algebra

J-Mester 2016

  • MTH 145 Calculus I (Online)

Spring 2016

  • MTH104 Mathematics for Decision Making
  • MTH 261 Linear Algebra
  • Independent Study on Advanced Linear Algebra

Summer 2016

  • MTH 145 Calculus I (Online)

Fall 2016

  • MTH 261 Linear Algebra
  • MTH 306 Topics in Number Theory -- Elementary properties of integers, divisibility and related concepts, methods of representing integers, functions of number theory, simple diophantine equations, special sequences and series. Offered every other fall.
  • MTH 341 Abstract Algebra

J-Mester 2017

  • MTH 145 Calculus I (Online)

Spring 2017

  • Sabbatical

Summer 2017

  • MTH 145 Calculus I (Online)

Fall 2017

  • MTH 261 Linear Algebra
  • MTH 341 Abstract Algebra

J-Mester 2018

  • MTH 145 Calculus I (Online)

Spring 2018

  • MTH 370 Intermediate Problem Solving

Summer 2018

  • MTH 145 Calculus I (Online)

Fall 2018

  • MTH 261 Linear Algebra
  • MTH 341 Abstract Algebra

J-Mester 2018

  • MTH 145 Calculus I (Online)

Spring 2019

  • MTH 120 Mathematics for Business Majors

Summer 2019

  • MTH 145 Calculus I (Online)

Fall 2019

  • MTH 261 Linear Algebra
  • MTH 341 Abstract Algebra