Here are a few of the
mathematics courses
offered at Hollins.

 

  "I never knew mathematics could be this interesting...cool topics!"

from '03 student enrolled in Laboratories in Mathematical Experimentation. 

 

 


Math 350 (new in 2003)
Explorations in Analysis - Fractals

This course is an exciting mathematical study of convergence and limits.  Students actively investigate concepts using numerical techniques followed by precise and careful analysis.  Topics include fractals, linear and nonlinear function iteration, basins of attraction, chaos, complex numbers and Newton's method.



Math 246 (new in 2003)
Laboratories in Mathematical Experimentation

This is a course in mathematical discovery.  Students "do" mathematics by designing mathematical experiments, obtaining mathematical results, analyzing data and making mathematical conjectures.  Students are exposed to several very different fields of mathematics including fractals, game strategy, coding theory, graphs and networks, function iteration and chaos.

 

"Hollins does an excellent job in teaching students how to analyze, think, and write intelligently."

from '97 Hollins mathematics major.

 

Math 241
Calculus I


This course starts with a very simple question:  How do we define the slope of a graph that is not a straight line?  This leads to the study of limits, derivatives, rules of differentiation, and applications of the derivative.  Students actively investigate all concepts from graphic, numeric, and algebraic points of view.  Weekly computer lab sessions are an integral part of the course.  Students also apply these concepts to real world problems:  Can you mathematically argue the McDonalds hot coffee lawsuit?  Can you find the most economical path through marsh land and dry land for an oil pipeline?  Can you design a window that allows a maximum amount of light?
Math 242
Calculus II


This course also starts with a very simple question:  How do we find areas of  “weird” regions?  This leads to the study of area under curves, antiderivatives, integrals, techniques (exact and approximate) of integration, and applications of the integral.  Students are actively engaged in the material through group projects, computer lab sessions, and class presentations.  Students apply these concepts to real world problems:  Can you design an attractive floor tile pattern and then determine the amount of paint required?  Can you determine exactly the volume of a pear or banana?  After integration, students are introduced to infinite sequences and series.
"It turns out mathematical proofs and legal arguments are quite similar."

from '94 Hollins mathematics major.

Math 310
Transition to Advanced Mathematics

In this course, students learn how to discover mathematics. Many students incorrectly believe that much of mathematics is the result of “divine inspiration” but nothing could be further from the truth.  Students learn that the first step in discovering mathematics is experimentation.  Using trial and error and intuition, students “experiment” until they recognize a pattern.  Then students learn to formulate a conjecture (of the pattern) and to formally prove the conjecture using direct proofs, proofs by induction, proofs by contradiction and/or  proofs by contraposition.  Mathematical topics covered include set theory, number theory, functions, function iteration and CHAOS! 

 

 

Math 372
Introduction to Real Analysis

In this course, students take a more detailed look at the ideas from single variable calculus.  Emphasis of this course is on comprehension, construction and communication, both written and oral (see above), of  formal mathematical proofs.  Students are active learners.  They present proofs on the board, they critique other students' proofs, and they lead class discussions.  Topics in the course include sequences, limits, continuity, differentiation, and integration.