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Academics
A "User's Guide" to selecting a first course
There
are many ways to begin the study of the mathematical sciences at Mount
Holyoke College. Students can begin with calculus, an introduction to
statistics or data analysis, an “explorations” course, or
computer science.
Calculus isn’t for everyone, but it is recommended or required for many majors and graduate programs, including economics, statistics, and most pure and applied sciences. Students who intend to study calculus at Mount Holyoke are strongly encouraged to complete precalculus (or a comparable course) before they arrive.
The department asks all students who are considering enrolling in calculus or statistics during their career at Mount Holyoke to complete a brief self-assessment on precalculus skills. Sample questions, with answers, are available at http://www.mtholyoke.edu/acad/math/pretest/pretest.htm. Competency in these basic skills is very important in quantitative courses throughout the Mount Holyoke curriculum, and students can profit from addressing any weaknesses before arriving on campus. The department also offers a noncredit mathematics refresher during January Term. The actual self-assessment is available to all entering students and all students preregistering for calculus. It is designed so that a student can use it as a learning tool, taking it as many times as she wishes, and getting pointers to appropriate review materials for the topics of any questions she misses.
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Beginning with calculus.
Many students begin their study of mathematics with calculus. If your interests lie in science or social science, calculus is important, because it is the language these disciplines use. Unlike many high school calculus courses, ours emphasize not only technical skills but also the concepts of calculus, the contexts in which the mathematical ideas arise, and realistic applications. Mastering the subject at this deeper level can be hard work, but the rewards are great, as students acquire meaningful, practical knowledge.
If you wish to begin with a calculus course, you can take one of the following courses:
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Mathematics 100A&B, Enriched Calculus 1A and 1B
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Mathematics 101, Calculus I
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Mathematics 202, Calculus II or
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Mathematics 203, Calculus III
The year-long course Enriched Calculus IA and IB includes all of the topics in Mathematics 101, Calculus I. It is intended for students who, based on the results of their precalculus assessment and the agreement of the instructor, need to strengthen their quantitative and algebraic precalculus skills in order to learn calculus effectively.
Students who have not studied calculus and who have the necessary precalculus background belong in Calculus I (101). Because some sections of Calculus I differ significantly from traditional high school calculus, it has been our experience that students who “start over,” in order to ease the transition into college, initially may have more difficulty in Calculus I than beginners. However, students who take Calculus I expecting and welcoming new ideas have found it rich and rewarding.
Most students who have taken calculus in high school begin with Calculus II (202). In particular, if you have studied the derivative and its applications and have been introduced to the definite integral, you will be prepared for Calculus II.
If you have a good knowledge of applications of integration and of transcendental functions, and if you enjoy mathematics, we encourage you to begin your college-level study of calculus with Calculus III (203). (The study of series is neither required for nor included in Calculus III. Physics and mathematics students will encounter this topic in other courses.)
Beginning the study of calculus beyond 101 does not require the advanced placement (AP) examination, although the score on this examination is a useful guide. A student with an advanced placement AB score of 3 or less should consider Mathematics 101 (Calculus I); an advanced placement AB score of 4 or 5 or a BC score of 3 indicates readiness for 202; a grade of 4 or 5 on the BC examination indicates readiness for 203.
Other Beginnings:
The “explorations” courses in algebra, number theory, geometry, fractals and chaos, and cryptology (110, 114, 120, 125, 139) offer another way to begin your study of mathematics. They emphasize mathematics as an art and as a way of seeing and understanding. The exploration courses do not presuppose special talent for or prior strong interest in mathematics. They intend to awaken interest by demonstrating either the remarkable pervasiveness of mathematics in nature and its power as a tool that transcends disciplines, or its qualities as an art that can fascinate and offer aesthetic pleasure to the participant. At least two and usually three of these exploration courses are offered each year.
A few students begin their study of mathematics with Linear Algebra (211) or the Laboratory in Mathematical Experimentation (251). Linear Algebra is a good choice for students who have a very solid background in high school mathematics and who enjoy abstraction. If you have taken some calculus, and if you enjoy exploring ideas on your own, then you might consider the Laboratory (251).
Finally, some students begin their study of mathematical sciences with statistics and computer science. For more information see the sections on statistics and computer science in this guide.
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Course Descriptions
MATH 100Af - 100Bs Calculus: Features modeling of phenomena in the natural and social sciences. Math 100A: representation and interpretation of data, functions and their graphs, the derivative. Math 100B: integrals and the varied processes that they can represent, accumulation and antidifferentiation, the several forms of the fundamental theorem, additional topics in differential equations with applications.
The year-long sequence 100A-B satisfies a single Science and Math II-A distribution requirement. Math 100-A alone does not meet a distribution requirement. Prereq. permission of instructor. Students may send assessment score and background information to Harriet Pollatsek (hpollats@mtholyoke.edu). 2 meetings (75 minutes), 1 meeting (50 minutes); 4 credits each semester; enrollment limited to 30
MATH 101fs Calculus I: Students who have not studied calculus and who have the necessary precalculus background belong in Calculus I. Because some sections of Calculus I differ significantly from traditional high school calculus, it has been our experience that students who "start over," in order to ease the transition into college, initially may have more difficulty in Calculus I than beginners. However, students who take Calculus I expecting and welcoming new ideas have found it rich and rewarding.
This course presents rates of change and their applications, integrals, the fundamental theorem, and modeling of phenomena in the natural and social sciences.
Meets Science/Math II-A requirement; 4 credits; 2 meetings (75 minutes), 1 meeting (50 minutes)
MATH 110f Explorations in Algebra: High school algebra is essentially the study of the laws that govern the system of numbers we use for ordinary arithmetic. This course focuses on certain of these laws and studies the systems, called "groups," governed by them. Groups have beautiful properties and describe many phenomena: crystallography, graphic art, matrix algebra, counting, nuclear physics, codes, and more. The course studies the group laws and their consequences, as well as many examples of systems meeting these laws.
Meets Science/Math II-A requirement; 4 credits; 3 meetings (75 minutes); enrollment limited
MATH 202fsCalculus II: Topics include techniques of integration, applications of integration, differential equations, sequences, series, and Taylor series.
Meets Science and Math II-A
requirement. Prereq. Mathematics 101 or equivalent, permission of department,
2 meetings (75 minutes), 1 meeting (50 minutes); 4 credits
MATH 203fs Calculus III: If you have a good knowledge of applications of integration and of transcendental functions, and if you enjoy mathematics, we encourage you to begin your college-level study of calculus with Calculus III.
Topics include differential and integral calculus of functions of several variables.
Meets Science/Math II-A requirement; 4 credits; 2 meetings (75 minutes), 1 meeting (50 minutes)
MATH 211fs Linear Algebra: Topics include elements of the theory of matrices and vector spaces.
Meets Science/Math II-A requirement;
Prereq. any 100-level mathematics course; 4 credits; 2 meetings (75 minutes)
MATH 251fs Laboratory in Mathematical Experimentation: (Writing-intensive course) Offers mathematics as a laboratory science. After a short introduction to the computer, uses hand and computer computation to explore mathematical ideas. Directs laboratory projects toward discovery of properties and patterns in mathematical structures. The choice of projects varies from year to year and is drawn from algebra, analysis, discrete mathematics, geometry, and statistics.
Meets Science/Math II-A requirement; Prereq. Mathematics 202 or equivalent, or permission of instructor; 4 credits; 2 meetings (2 hours)