Spring 2012

MATH 1150 Math Foundations Seminar, Perspectives in Art, Natasha Dobrinen
Section 1, CRN 2826, 15 students, Meets MW 10-11:50AM in JGH219
Section 2, CRN 2827, 15 students, Meets MW 12-1:50PM in JGH219

Perspectives in Art is a course in the mathematics of perspective and fractal geometry in art. We will use a new book developed for liberal arts mathematics called, Viewpoints, by Marc Frantz and Annalisa Crannell. We will cover 1, 2, and 3-point perspective and fractal geometry. Perspectives are tools to help artists draw objects more accurately. Fractals occur in nature and can be used to draw life-like images of plants, trees, coastlines, and more. Upon completion of the course, students will have mathematical, and some artistic, tools to draw accurate renditions of geometric objects such as buildings and roads from different angles, fractal-like objects such as snowflakes and trees, and have a better appreciation for art. Basic algebra skills and knowledge of logarithms will be assumed.

MATH 1150-3 Math Foundations Seminar, Mathematics of Games, Ronnie Pavlov
CRN 2828, 15 students, Meets TR 10-11:50AM in JGH 219

Most of us have played games such as Tic-Tac-Toe, chess, Go, and checkers. Many games can be studied mathematically using a branch of mathematics called game theory. We will discuss various facets of elementary game theory, including (but not limited to!) how to formulate strategies, what makes some strategies “better” than others, what makes some games difficult or impossible to analyze, and applications to real-world concepts such as economics, political science and anthropology. Specific topics we will cover include the Nash equilibrium, the prisoner’s dilemma, and bluffing in poker.

The class will not be purely theoretical; we will spend lots of time applying the course concepts by playing various games. A homework assignment might involve analyzing a simple game, devising a winning strategy, and then trying it out during class.

The only prerequisites are basic skills in algebra and geometry and a healthy interest in problem/puzzle solving. We may use some simple concepts from linear algebra and probability during the course, but these will be developed as they are needed.

MATH 1150-4 Math Foundations Seminar, Graph Theory in the Real World, Allegra Reiber
CRN 3142, 30 students, Meets MW (10-10:50AM) in JGH 102
(This is a hybrid course. A significant portion of the course work occurs online.)

A graph in its simplest form is merely a collection of dots, called vertices, and a collection of line segments, called edges, running between some or all of the vertices. The graph could model the walking paths on campus, the preferred pizza toppings of a group of friends, or an abstract mathematical relationship. During this course, we will study the concepts and results of graph theory, how to solve problems related to graphs, and how solving graph theory problems helps us understand real world problems: scheduling, map coloring, postal delivery routes, amicable seating charts, population life cycle analysis, DNA sequencing, and more. Coursework will include reading and writing mathematical arguments about graphs; making calculations related to graphs; utilizing the Mathematica software package to understand graph theory concepts; and discovering relevant real-world applications of graph theory. This is a hybrid course, meaning that some of the course meetings are face-to-face, on Mondays and Wednesdays, while on Tuesdays and Thursdays, you will engage with course content, complete assignments, and communicate with classmates and the instructor through our Blackboard course. No specific mathematics knowledge is presumed, but strengths in reading, writing, and reasoning will be necessary to succeed with assignments and use of Mathematica.

Previously offered seminars

• 2, Infinity & Beyond (Carney, Ormes)
• Cryptography (Arias, Curran, Vojtechovsky)
• Games and Logic (Galatos)
• Graph Theory (Zenk)
• Graph Theory in the Real World (Locke, Reiber)
• Great Ideas in Mathematics (Trujillo)
• Heart of Mathematics (Pula)
• Logic and Games (Galatos)
• Mathematical Art (Gudder)
• Mathematics for Decision Making (Ormes)
• Mathematics in Art and Music (Dobrinen)
• Mathematics of Chance (Latremoliere)
• Mathematics of Chance and Gambling (Arias)
• Mathematics of Gambling (Arias, Gudder, Hagler)
• Mathematics of Games (Pavlov)
• Mathematics of Politics (Hagler)
• Mathematics of Voting (Hagler)
• Models of Computing (Ball)
• Non-Classical Logics (Galatos)
• Patterns and Symmetry (Ormes)
• Perspectives in Art (Dobrinen)
• Pi: The Story of a Number (Kinyon)
• The Geometry of the Universe (Latremoliere)
• Thinking Machines (Ball)