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.
Algebra – MA 101 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
Precalculus – MA 102 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.
Elementary Statistics – MA 103 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.
Calculus & Analytic Geometry 1 – MA 106 Amos Carpenter
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.
Calculus & Analytic Geometry 1 – MA 106 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.
Calculus & Analytic Geometry 1 – MA 106 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.
Calculus II – MA 107 Lacey Echols
Why a Liberal Arts Education: The liberal arts education at Butler University seeks to enhance communication skills and critical thinking. In calculus your communication skills will be improved by written presentations and explanations for problem solutions, and your critical thinking skills will be honed by the application of calculus concepts in various fields. 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. In almost no other discipline is it as important to communicate precisely as it is in mathematics. Mathematics is a language, and you are learning the language of calculus. You will be learning how to draw logical conclusions for a variety of different mathematical situations, developing your ability to apply calculus methods. The communication and critical thinking skills you learn will enhance your success in all of your other courses and in turn enrich your future endeavors.
Linear Mathematics and Calculus – MA 119 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.
Discrete Mathematics 1 – MA 205 Prem Sharma
The main objective of this course is to learn some of the most fascinating combinatorial ways of enumeration. The ingenuity and elegance of such notions as the Rook polynomials and Ferrer graphs is simply enchanting. Also, the concepts learnt in this course are essential to most branches of mathematics. The beautiful mathematics encountered in this course makes it a most befitting choice in a wholesome liberal arts curriculum.
Active-Learner Credit (A-L C): The best way to learn mathematics is by learning to think mathematics. For example, a proof is best learnt by thinking through it rather than cramming it. It is particularly important in this course that you avoid cramming and strive to think through the counting arguments. To insure that you learn on a continuous basis, the class will be given a brief oral quiz each day we meet. This practice should instill in you a habit of thinking and assimilating mathematics continuously.
Calculus and Analytic Geometry 3 – MA 208 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.
Statistical Methods – MA 260 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.
Real Analysis 1 – MA 326 Prem Sharma
The main objective of this course is to study the notions of convergence, continuity, and compactness in the abstract metric space setting. As enunciated by the Mathematical Association of America (briefly the MAA) in its two most recent studies [CUPM 1995 and CUPM 2004], the foremost learning goal in an Undergraduate Mathematics Program is:
the students should progress from a procedural/computational understanding of mathematics to a broad understanding encompassing logical reasoning, generalization, abstraction, and formal proof.
I have chosen the abstract metric space setting for this course for two reasons: first, it admirably meets the MAA recommendation, and second, this is by far, the most elegant (and also, the most challenging!) way to study mathematical analysis. The immense intellectual challenge posed and the sheer elegance of abstractions encountered in this course far exceed those in any other Undergraduate mathematics course. For these qualities, this is a course that any liberal arts curriculum can be most proud of.
*Textbook. Since its first publication in 1953, Walter Rudin's Principles of Mathematical Analysis (now in its 3rd edition) has been the most loved and admired textbook in Analysis not only in the U.S. but throughout the world. Consider the fact that though the MAA assiduouly tries not recommending any textbooks for any undergraduate courses, they had to make an exception in this case and they heartily recommended Rudin. Unfortunately, it has become nearly impossible to implement this recommendation. It is a shame that the overall students' mathematical preparation in High School and through their initial two-three years has fallen so precipitously that most colleges find it unfeasible to use this excellent book. As woeful as the current state of affairs is, I still continue to prescribe Rudin as I often feel deeply inspired by Tennyson's Ulyssis:
Though much is taken, much abides; and though
We are not now that strength which in old days
Moved earth and heaven, that which we are, we are-
One equal temper of heroic hearts,
Made weak by time and fate, but strong in will
To strive, to seek, to find, and not to yield.
What is Expected: By the end of the semester, I expect you to be able to (1) Understand the Definition-Theorem-Proof trinity of proof writing (2) Read, with full comprehension, the prescribed textbook (3) Write clear, correct, and concise proofs.
Differential Equations – MA 334 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.
Topology – MA 354 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.
Stochastic Process Models – MA 371 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.