MA 101 - Algebra ~ View
Section Statements
MA 101 - Algebra - Karen Holmes ~ View Section Statements
Karen Holmes
Most people wonder when on earth they're ever going to need to
use the Quadratic Formula that their algebra professor made them
memorize. The answer is that other than MA102 or whatever other
math class you'll be taking, you'll probably never see it again!
So, why is MA101 part of a liberal arts education? Math, in
general, is not just dealing with numbers, but processes to reason
through problems. Those problems could be managing your time,
balancing your budget, or even which route to take home. If you
have a solid method of how to solve problems, you can make many
aspects of your life easier. We hope that by understanding how and
when to use the Quadratic Formula that someday this will help you
make larger life decisions.
MA 101 - Algebra - Donald Minassian ~ View Section Statements
Donald Minassian
Mathematics, and the logical thinking flowing there from, is
deemed an integral part of a liberal education. In MA101 you will
have "story problems" calling for analyzing the problem and writing
the proper equations. Our hope is that such logical thinking will
translate into other areas such as evaluating political statements,
commercial advertisements, business plans, and the like
MA 102 - Precalculus ~ View
Section Statements
Karen Holmes
Most people wonder when on earth they're ever going to need to
use the Quadratic Formula that their algebra professor made them
memorize. The answer is that other than whatever other math class
you'll be taking next, you'll probably never see it again! So, why
is MA102 part of a liberal arts education? Math, in general, is not
just working with numbers, but processes to reason through
problems. Those problems could be managing your time, balancing
your budget, or even which route to take home. If you have a solid
method of how to solve problems, you can make many aspects of your
life easier. We hope that by understanding how and when to use the
Quadratic Formula that someday this will help you make larger life
decisions easier.
MA 103 - Elementary Statistics ~ View
Section Statements
Karen Holmes
You can hardly read a newspaper or article on the web, watch a
baseball game or any other sporting event, or listen to a newscast
on TV or radio without hearing statistics mentioned. MA103 will
help you understand where the statistics come from and what they
mean which will help you make more informed decisions or opinions
on whatever the matter may be. Some of those decisions can be very
important, such as should you take a certain drug given the side
affects in a certain percentage of the participants in a clinical
drug trial. Nearly every discipline makes use of statistics
somehow, so liberal arts-wise statistics has very broad use.
MA 104 - Introduction to Contemporary Math ~ View Section Statements
Prem Sharma
Calculus is a prerequisite for almost all branches of
mathematics. This course will help you develop problem solving and
critical thinking skills. This will be achieved by solving the
assigned problems. By using the language of mathematics to solve
these problems and write down your answers you develop the
necessary communication skills. Many of the problems you solve will
come from science, engineering, business, and even industry. So you
will also be analyzing knowledge from other disciplines.
MA 106 - Calculus & Analytic Geometry 1 ~
View Section
Statements
MA 106 - Calculus & Analytic Geometry 1 - Duane
Leatherman ~ View Section Statements
Duane Leatherman
It has been said that mathematics is the language with which the
universe is written. Specifically, calculus has been called the
most important computational invention in history. Thus,
mathematics is an underlying foundation for most disciplines of
human endeavor. It is therefore essential for individuals to
possess the critical and analytical thinking skills needed to
function in a world heavily dependent on mathematical concepts. A
liberal arts university, such as Butler, is a perfect place for
those skills to be developed and fostered because those are some of
the exact skills which are the goals of a liberal arts education.
This course will attempt to help strengthen your math skills while
also developing a broader appreciation for calculus which has led
to the technological society of today.
MA 106 - Calculus & Analytic Geometry 1 - Scott
Parsell ~ View Section Statements
Scott Parsell
Does it make sense to talk about the speed of an accelerating
object? Can we measure the exact area of a region with curved
boundaries? How is it possible to complete a task if we must do
half of the remaining work infinitely many times? These are some of
the deep philosophical questions that motivated the development of
calculus. This course emphasizes the thought processes used to
resolve these issues and highlights the power and beauty of the
resulting ideas. We will develop the critical thinking skills
necessary to deduce useful consequences of the theory and also to
identify situations in which it does not apply. Effective written
communication that clearly conveys our problem-solving strategies
and the logical flow of our arguments will be extremely important.
While calculus is often viewed as a tool for use in other
disciplines, we will find that it has a rich structure that makes
it worth studying for its own sake as part of a liberal
education.
MA 106 - Calculus & Analytic Geometry 1 - Chris
Wilson ~ View Section Statements
Chris Wilson
Calculus is one of the most important and versatile branches of
mathematics. Calculus gives precision to the notion of how fast a
quantity is changing, and this notion leads to a wealth of
information about the behavior of mathematical functions. The study
of calculus offers many students their first glimpse of the beauty
and interconnectedness of mathematical ideas. You will not only
improve your ability to think logically and to articulate
information clearly, but you will encounter one of the greatest
"big pictures" ever discovered.
MA 106 - Calculus & Analytic Geometry 1 - Scott
Parsell ~ View Section Statements
Scott Parsell
Does it make sense to talk about the speed of an accelerating
object? Can we measure the exact area of a region with curved
boundaries? How is it possible to complete a task if we must do
half of the remaining work infinitely many times? These are some of
the deep philosophical questions that motivated the development of
calculus. This course emphasizes the thought processes used to
resolve these issues and highlights the power and beauty of the
resulting ideas. We will develop the critical thinking skills
necessary to deduce useful consequences of the theory and also to
identify situations in which it does not apply. Effective written
communication that clearly conveys our problem-solving strategies
and the logical flow of our arguments will be extremely important.
While calculus is often viewed as a tool for use in other
disciplines, we will find that it has a rich structure that makes
it worth studying for its own sake as part of a liberal
education.
MA 106 - Calculus & Analytic Geometry 1 - Pisheng
Ding ~ View Section Statements
Pisheng Ding
Calculus is the mathematical tool for describing and studying
change. Its principles underlie many disparate phenomena. The
mechanical state of a system of particles, the population size of a
species in nature, the level of concentration of a medication in
the human body, and many such quantifiable variables arising from
sciences can all be subjected to rigorous analysis by Calculus when
one takes into account both the laws governing how these variables
change and the constraints the environment imposes on them.
The English physicist/mathematician Sir Isaac Newton (1642-1727)
conceived Calculus to elucidate the laws of motions and the
"clockwork" of the/his universe. A philosophical implication of
Newtonian physics is a deterministic view of the universe: knowing
the current state of the universe, one can predict, with precision,
the course of evolution of the universe and hence the state of the
universe at any future point in time. Calculus was directly
responsible for this school of philosophical thought; Calculus will
also bring this paradigm to its demise in our contemporary
time!
In fact, laws of physics are most often expressed in the
language of Calculus, and they all carry significant metaphysical
weight (just as Newton's laws do), which can only be fully
appreciated if one is Calculus-literate. Therefore, Calculus opens
up for you a whole new world!
MA 107 - Calculus II ~ View Section
Statements
Pisheng Ding
Calculus is the mathematical tool for describing and studying
change. Its principles underlie many disparate phenomena. The
mechanical state of a system of particles, the population size of a
biological species, the level of concentration of a chemical in the
human body, and many such quantifiable variables arising from
sciences can all be subjected to rigorous analysis by Calculus when
one takes into account both the laws governing how these variables
change and the constraints the environment imposes on them.
The English physicist/mathematician Sir Isaac Newton (1642-1727)
conceived Calculus to elucidate laws of motions and the "clockwork"
of the/his universe. A philosophical implication of Newtonian
physics is a deterministic view of the universe: knowing the
current state of the universe enables one to predict, with
precision, the course of evolution of the universe and hence the
state of the universe at any future point in time. Calculus was
directly responsible for this school of philosophical thought;
Calculus also brings about the demise of this paradigm in our
contemporary time!
In fact, laws of physics are most often expressed in the
language of Calculus, and they all carry significant metaphysical
weight (just as Newton's laws do), which can only be fully
appreciated if one is Calculus-literate. The language, method, and
philosophy of Calculus are key to any serious attempt to describe
and understand the seeming chaos and underlying patterns of the
universe (social and physical) we live in!
MA 119 - Linear Mathematics and Calculus ~ View Section Statements
Joe Fischer
Critical thinking and effective communication are emphasized in
Butler's mathematics courses, for these skills are at the heart of
a liberal arts education where logic is the driving force. In this
course, problems are considered in a broad context demonstrating
how the study of mathematics is not only an end in itself, but also
how mathematics provides the necessary quantification tools for
other fields of study. Business applications receive special
emphasis.
MA 125 - Business Calculus ~ View Section
Statements
Chris Wilson
Calculus is one of the most important and versatile branches of
mathematics. Calculus gives precision to the notion of how fast a
quantity is changing, and this notion leads to a wealth of
information about the behavior of mathematical functions. Calculus
is the mathematical tool that helped challenge notions about the
earth's place in the solar system, and it is also a tool that has
many applications in business, as we will see this semester.
The study of calculus offers many students their first glimpse
of the beauty and interconnectedness of mathematical ideas. You
will not only improve your ability to think logically and to
articulate information clearly, but you will encounter one of the
greatest "big pictures" ever discovered.
MA 162 - Statistical Methods ~ View Section
Statements
Chris Wilson
Statistics is one of the most widely used branches of
mathematics. Business decisions and government policies are based
on the analysis of statistical data. Published research in the
physical and social sciences is usually supported by data analysis.
In this course, you will learn techniques for producing and
analyzing data that have applications in a variety of disciplines.
Statistics provides a precise language with which one can draw
inferences about a large population based on a small sample. Your
study of statistics will also sharpen your critical thinking skills
as you interpret mathematical information in a real-life context
and learn to determine the validity (or lack thereof!) of
conclusions that appear to be drawn from statistical data.
MA 200 - Basics of Advanced Mathematics ~ View Section Statements
MA 200 - Basics of Advanced Mathematics - Judi
Morrel ~ View Section Statements
Judi Morrel
Among other goals, the liberal arts education at Butler
University seeks to enhance skills of communication and critical
thinking. In this course, as in other higher-level mathematics
courses, your critical thinking skills will be honed by the use of
logic and the techniques of mathematical proof, and your
communication skills will be improved by the written presentations
and oral explanations of proofs and solutions. In fact, in almost
no other discipline is it as important to communicate precisely as
it is in mathematics. From one point of view, mathematics is a
language and a proof is one of the basic forms of communication in
that language. Another hallmark of a liberal arts education is the
development of an intellectually curious mind together with the
ability to come to well-reasoned conclusions for oneself.
Ascertaining the truth or falsehood of mathematical statements is
an analytical process and practice in doing so will improve your
ability to consider critically the validity of any argument, be it
mathematical or not. Constructing proofs develops your capacity to
build arguments, use evidence, and draw correct conclusions; each
of these abilities is vital for liberally educated citizens in the
21 st century.
MA 200 - Basics of Advanced Mathematics - Prem
Sharma ~ View Section Statements
Prem Sharma
Course Objectives: This course is intended to serve as a gateway
to higher mathematics. The course begins by introducing the
language of mathematical logic and rules of inference, and then it
proceeds to the study of main properties of axiomatically defined
structures such as partial orders, well-orderings, and equivalence
relations. We study Cantor's theorem concerning infinite cardinal
numbers and the natural ordering on the cardinals. The course
stresses the importance of a definition in the
Definition-Theorem-Proof trinity. Such mighty abstract ideas
cultivate the mind and enrich the study of Liberal Arts.
MA 205 - Discrete Mathematics 1 ~ View Section Statements
Prem Sharma
This course introduces several combinatorial concepts such
permuatatoins, combinations, rook polynomials, Stirling numbers
(second kind), recursive definitions and generating functions. The
Inclusion-Exclusion Principle and the Pigeonhole Principle are
studied in depth. The subject matter cultivates a student's
critical thinking skills to distinguish between seemingly identical
yet profoundly diffentent concepts frequently encountered in this
course.
MA 206 - Discrete Mathematics 2 ~ View Section Statements
Prem Sharma
This course introduces the notion of an abstract graph. Various
concepts relating to a graph such as a path, a trail, a cycle are
studied. Applications of graph theory to transport networks,
optimization theory, matching theory, physiology, chemistry, and a
host of other fields of study are discussed. But even apart from
all its important applications, graph theory is a must-study for
its sheer elegance and richness of ideas that make it a most
befitting component of a wholesome Liberal Arts curriculum.
MA 208 - Calculus & Analytic Geometry 3 ~
View Section
Statements
Prem Sharma
The main objective of this course is to develop an understanding
of the linear and differential structure of the 3-dimensional
Euclidean space. Notions of curves and surfaces; gradient,
direction and motion; double and triple integrals; and areas and
volumes are developed. This course, as a purely intellectual
pursuit and as a gateway to a journey into highly abstract spaces
wherein the notions of dimension, direction, and gradient carry no
meaning at all is befitting the true meaning of liberal arts.
Active-Learner Credit (A-L C): You learn mathematics best by
assimilating it continuously on a regular basis rather than
cramming it for a day for the purpose of passing an examination. To
be good at mathematics, one has to learn to think mathematics.
Students given to mindlessly stuffing their brains with facts and
formulas cannot be good at doing or teaching mathematics as they
fail to conceive the poetic beauty in mathematics.
MA 260 - Statistical Methods ~ View
Section Statements
Lacey Echols
Why a Liberal Arts Education: A liberal arts education should be
one in which you learn to think for yourself and apply all that you
have learned from various fields of learning to solve problems and
be creative with new ideas. At Butler University, there is an
effort to provide you with knowledge in various subjects so that
you can understand how processes and ideas fit together. Learning
statistics will facilitate this experience in several ways,
including exercising and strengthening the more quantitative and
analytic aspects of your intellect and providing you with a
framework by which you can interpret and evaluate research produced
by any of the scientific disciplines. Statistics is used in most
fields, including business, education, the natural sciences,
pharmacy, and almost all other subjects. Statistics will help you
understand everyday phenomena and phenomena that probably will
never occur! This subject will prepare you for any undergraduate
research or graduate research. It will strengthen your logical
thought processes and enable you to be a well-educated liberal arts
graduate of Butler University.
MA 311 - Number Theory ~ View
Section Statements
Scott Parsell
For more than two thousand years, scholars have sought to better
understand the structure of the integers. Questions about the
distribution of primes or the existence of integer solutions to the
equation x^3+y^3=z^3, for instance, are usually motivated by
genuine intellectual curiosity rather than by the potential for
real-world applications. Over the past 30 years, number theory has
proven to be incredibly useful for public-key cryptography, but it
remains a subject studied more for its own inherent beauty than for
any other purpose. Starting with a few basic axioms, we can deduce
many striking results, and yet many fundamental questions remain
completely unresolved. Each new development provides some answers
but also new questions that open new lines of inquiry and keep the
subject thriving. This robust set of interconnected facts and
boundless mysteries makes number theory an ideal subject for study
as part of a liberal arts education.
MA 312 - Modern Algebra I ~ View
Section Statements
MA 312 - Modern Algebra I - Scott Parsell ~ View Section Statements
Scott Parsell
In common with many other liberal arts subjects, this course
emphasizes abstract ideas, critical thinking, and logical
reasoning. The theory of groups that we will develop unifies many
branches of mathematics and is well worth studying for its own
inherent beauty. Amazingly, this abstract theory also fosters
connections across the liberal arts by providing elegant
descriptions of naturally occurring symmetries.
MA 312 - Modern Algebra I - Prem Sharma ~ View Section Statements
Prem Sharma
This course introduces a number of axiomaitically defined
algebraic structures such as a group, a ring, and a field. The
group structure is studied in detail as we consider the concepts of
a subgroup, a normal subgroup, a quotient group, and a group
homomorphism. The groups of symmetries of several familiar
geometric objects (e.g., the Platonic solids and several plane
figures) are determined. Many important theorems in Group Theory
including the Lagrange Theorem, the Sylow Theorems, Caley's
Theorem, and the homomorphism theorem are studied. This course is a
testament to the power of abstract mathematics as it reveals so
many deeply-hidden secrets about things of the old. The rich
content of this course greatly enhances the sublimity of a Liberal
Arts education.
MA 312 - Modern Algebra I - Pisheng Ding ~ View Section Statements
Pisheng Ding
Modern Algebra Is Painfully Abstract but Nonetheless
Liberating!
The rapid growth of mathematics in the 19th century resulted in
a vast body of mathematical knowledge. It became increasingly
apparent that many disparate mathematical phenomena bore structural
similarities that could not be mere coincidences. The turn of the
20th century marked a clear departure from classical mathematics.
Mathematics in the new century no longer dwelled on concreted
objects, individual facts, and ad hoc methods; it sought higher
levels of abstraction aimed at synthesizing existing knowledge and
providing unifying frameworks for seemingly disconnected fields.
Many new disciplines such as set theory, functional analysis,
topology, bursted onto the scene. This higher level of abstraction
and higher standard of rigor in mathematics in turn reinvigorated
classical mathematics, yielding, on an industrial scale and in a
systematic fashion, new and previously unattainable results.
It is against this backdrop that modern algebra came to the fore
of mathematics to give organization and generalization to a
collection of mathematical knowledge pertaining to algebraic
operations in certain sets. In this course, you will be empowered
by mathematical abstractions, which may be initially painful but
will eventually turn fruitful; in the end, you will be far better
equipped to discern pattern and to internalize order in this
chaotic world - the very original purpose of mathematics or of any
meaningful intellectual endeavor.
MA 313 - Modern Algebra II ~ View
Section Statements
Phrem Sharma
This course builds upon the concept of a group studied in 1VIA
312. A new algebraic structure, called a ring, that has a richer
structure than that of an abelian group is introduced and several
gradation of rings such as integral domains, Euclidean rings,
principle ideal domains, unique factorization domains, and fields
are studied. After briefly discussing the fundamentals of the
theory of equations, Newton's identities are derived. We also study
the landmark work of the great genius Evariste Galois on field
extensions and solvability by radicals and we discuss how Galois'
amazing discoveries trivialized the classic theorem of Abel about
unsolvabitily of a general quintic. Among the purly number
theoretic results we study Fermat's Two Square Theorem, Legendre's
Three Square Theorem, and Lagrange's Four Square Theorem. The
course, offering us a glimpse into such great minds as Newton,
Fermat, Legendze, Lagrange, and Galois, is a mathematical jewel
that adorns the Liberal Arts education!
MA 315 - Linear Algebra ~ View
Section Statements
MA 315 - Linear Algebra - Judi Morrel ~ View Section Statements
Judi Morrel
As a discipline, mathematics is an integral part of a liberal
arts education. In medieval universities the seven liberal arts,
composed of the trivium and the quadrivium, were considered
essential to a quality education. Of these seven (grammar, logic,
rhetoric, arithmetic, geometry, music, astronomy), four are
mathematical in nature. In the 21st century, one of hallmarks of a
liberal education is the ability to solve complex problems, and
linear algebra in particular, teaches us schema to model complex
situations and manipulate the models to solve real-world problems.
The skills and concepts learned in this course allow us "to tackle
and solve increasingly difficult and challenging problems," surely
a desirable, even necessary, attribute of educated citizens. N.B.
The quoted material is from the College of Liberal Arts and
Sciences Core Values statement, the entirety of which may be found
at www.butler.edu/las/LAS_Core_Values_Statement.aspx
MA 315 - Linear Algebra - Rebecca Wahl ~ View Section Statements
Rebecca Wahl
The philosophy of a liberal arts education is based on the
belief that by studying the relationships among a few principle
disciplines, our minds develop the ability to identify patterns and
to make analogies and inferences in subjects seemingly far
removed.
Linear Algebra is the mathematics of applications in the modern
world. The power of modern computers coupled with the ability to
formulate real world applications as matrix theory questions, has
earned Linear Algebra its place (along with Calculus) among the top
two most important subjects in applied mathematics today. Similar
to the original philosophy of a liberal arts tradition, we will
focus on the theory of Linear Algebra so that we may return to our
diverse disciplines and render its application.
MA 326 - Real Analysis 1 ~ View
Section Statements
Prem Sharma
The main objective of this, course is to study the notions of
convergence, complete- ness, continuity, and compactness in the
abstract metric space setting. The Mathematical Association of
America has enunciated in its two most recent studies that the
foremost learning goal in an Undergraduate Mathematics Program is:
the students should progress from a procedural/computational
understanding of mathematics to a broad un- derstanding
encompassing logical reasoning, generalization, abstraction, and
formal proof. While the abstract metric space setting chosen for
this course admirably meets this MAA recommendation, it does
present the student an immense intellectual challenge and thus
requiring the utmost diligence on his part. However, the student is
amply rewarded for his tribulations and perseverance by the sheer
beauty of abstractions encountered in this course. In fact, this
course is, to a diligent student, a most exhilarating experience in
undergraduate mathematics. For all the beautiful abstractions and
elegant proofs encountered in it, this is a mathematics course that
any Liberal Arts Curriculum can be most proud of.
MA 327 - Real Analysis 2 ~ View
Section Statements
Prem Sharma
This course is a continuation of MA 326. It is, therefore, cast
in the same elegant metric space setting as its precursor. We
explore the such notions as a function space, pointwise
convergence, uniform convergence, a ring of sets, an abstract
measure, and a nonmeasurable set. The famous Birkhoff Transitivity
Theorem concerning chaotic functions is proved and some of its
consequences are examined. Mathematical ideas, sifted and refined
over two millennia, appear in this course in such abundance that it
exudes the true spirit of a Liberal Arts education.
MA 334 - Differential Equations ~ View Section Statements
Amos Carpenter
One definition of a liberal arts education is a program of study
that encourages critical thinking, communication, quantitative
reasoning (including logic and problem solving), and the analysis
of knowledge from other disciplines. Differential equations are the
mathematical backbone of many areas of science and engineering. In
this course, we will describe or model the behavior of some systems
or phenomenon in mathematical terms and solve the resulting
differential equation or system of differential equations. The
system or phenomenon we consider will come from science (biology,
chemistry, and physics), engineering, economics, and even
psychology. By doing this, we will be analyzing knowledge from
other disciplines. We will study different algorithms for solving
different types of differential equations or systems of
differential equations. This will offer valuable exposure to logic
and problem solving paradigms. You will use critical thinking and
communication to solve the assigned problems.
MA 354 - Topology ~ View
Section Statements
Judith Morrel
Among other goals, the liberal arts education at Butler
University seeks to enhance skills of communication and critical
thinking. In Topology, as in other higher-level mathematics
courses, your critical thinking skills will be honed by the use of
logic and the techniques of mathematical proof, and your
communication skills will be improved by the written presentations
and oral explanations of proofs and solutions. In fact, in almost
no other discipline is it as important to communicate precisely as
it is in mathematics. From one point of view, mathematics is a
language and a proof is one of the basic forms of communication in
that language. Another hallmark of a liberal arts education is the
development of an intellectually curious mind together with the
ability to come to well-reasoned conclusions for oneself.
Ascertaining the truth or falsehood of mathematical statements is
an analytical process and practice in doing so will improve your
ability to consider critically the validity of any argument, be it
mathematical or not. Constructing proofs develops your capacity to
build arguments, use evidence, and draw conclusions; each of these
abilities is vital for liberally educated citizens in the 21 st
century.
MA 365 - Numerical Analysis ~ View
Section Statements
Amos Carpenter
Numerical analysis is the study of algorithms for problems in
continuous mathematics. In this course, you will learn to identify
the types of problems that require numerical techniques for their
solution and see examples of the error propagation that can occur
when numerical methods are applied. By solving the assigned
problems you will develop problem solving and critical thinking
skills. By using the language of mathematics to solve these
problems and write down your answers you develop the necessary
communication skills. Many of the problems you will solve will come
from diverse areas of engineering, as well as from the physical,
computer, biological, and social sciences. The chosen applications
will clearly and concisely demonstrate how numerical techniques can
be, and often must be, applied in real-life situations.
MA 371 - Stochastic Process Models ~ View Section Statements
Donald Minassian
Mathematics, and the logical thinking flowing there from, is
deemed an integral part of a liberal education. In MA371 a great
deal of logical analysis is demanded, as many problems "stand on
their own." Also, of course mathematics is becoming more and more
foundational in many areas of science -- it has been called "queen
and handmaiden of the sciences" -- as well as economics, computing,
etc.