Mathematics

Mathematics has been called the language of the sciences and, more broadly, the most powerful tool for the analysis of patterns across all fields of study. The main mission of the Department of Mathematics is to promote an understanding of and appreciation for this vision of mathematics. Since the power of mathematics derives from both descriptive and inferential aspects it is important to consider the possibility for its misuse while emphasizing its enormous potential for good. In practice, students are expected to participate actively in both the formulation of mathematical questions and in trying to solve them, using appropriate mathematical methods. This goal includes the understanding that students will be expected to demonstrate mastery of the basic mathematical concepts and methods relevant to the questions they are trying to solve.

DEGREE OFFERED

The Bachelor of Science is offered in mathematics.

Mathematics Major

Bachelor of Science

The major requires a minimum of 32 credit hours (eight courses) in mathematics courses or seminars numbered above 120.

MATH 225 Multivariable Calculus - 4 credits
MATH 231 Foundations of Mathematics - 4 credits
MATH 325 Linear Algebra or MATH/PHYS 320 Mathematical Physics - 4 credits

CHOOSE ONE COURSE (4 credits)
MATH 335 Topology - 4 credits
MATH 430 Algebraic Structures - 4 credits
MATH 435 Real Analysis - 4 credits
MATH 475 Seminar in Mathematics - 4 credits

CHOOSE ONE COURSE (4 credits)
MATH 310 Probability and Statistics - 4 credits
MATH 412 Discrete Mathematics II - 4 credits
MATH 415 Numerical Analysis - 4 credits
MATH 475 Seminar in Mathematics - 4 credits

Three MATH courses above 120 - 12 credits

Total credit hours required for B.S. degree in mathematics – 32 credits

Many majors emphasize a particular area of mathematics in their course work. Those emphasizing theoretical mathematics have been notably successful in graduate study at respected universities; majors who wish to prepare for graduate school should take MATH 335, MATH 430 and MATH 435.

Other students emphasize applied mathematics in preparation for advanced study in areas other than mathematics; such majors should include MATH 310 and an advanced seminar MATH 475 on an applied topic of interest in their programs.

Students preparing to teach mathematics in secondary schools should take MATH 235, MATH 310 and MATH 430.

The most frequent double major with mathematics is physics; students pursuing this option should take MATH/PHYS 320 and an advanced seminar (MATH 475) on further topics in mathematical physics.

Mathematics majors are frequently double majors. Such majors that allow students to pursue other strong interests in any other discipline and relate them to mathematics are encouraged by the department.

Mathematics Minor

For the Sciences Minor

Mathematics is often called the language of the sciences. As such it provides a means by which scientists model that which they observe in the “worlds” they seek to describe and those simulated in their laboratory experiments. A primary means of such modeling is through the use of elementary functions whose analysis is a major focus of calculus.

Mathematics for the sciences is a minor within mathematics itself that provides students with the understanding of and techniques for modeling using the elementary functions and techniques of calculus. The minor is designed primarily for physics and other natural science majors who are interested in modeling or are preparing for graduate study. However, it is appropriate as well for some social science and business and policy study majors, especially those interested in economic systems.

The minor in mathematics for the sciences is not available to mathematics majors.

 The minor requires a minimum of 16 credit hours (four courses).

MATH 225 Multivariable Calculus - 4 credits
CHOOSE THREE COURSES (12 credits)
MATH 121 Calculus I - 4 credits
MATH 122 Calculus II - 4 credits
MATH 123 Accelerated Calculus - 4 credits
MATH 310 Probability and Statistics - 4 credits
MATH 320 Mathematical Physics - 4 credits
MATH 325 Linear Algebra - 4 credits
MATH 475 Seminar in Mathematics - 4 credits

Total credit hours required for mathematics for the sciences minor – 16 credits

Philosophy of Mathematics

The portals to Plato’s academy contained the message (paraphrased): “Let no one enter here who does not know mathematics.” As this quotation suggests, there is a rich history to the connections between mathematics and philosophy. The philosopher-mathematician tradition continues today and can be found in, among others, the theories of formalism, intuitionism and Platonism.

Philosophy of mathematics is a cross-disciplinary and cross-divisional minor that investigates the connections between philosophy and mathematics. It is particularly designed as a companion to either a philosophy or mathematics major.

The minor requires a minimum of 16 credit hours (four courses).

MAT 112 Elementary Statistics or MATH 310 Probability and Statistics - 4 credits
CHOOSE ONE COURSE (4 credits)
MATH 121 Calculus I - 4 credits
MATH 122 Calculus II - 4 credits
MATH 123 Accelerated Calculus - 4 credits
MATH 125 Multivariable Calculus - 4 credits

MATH 231 Foundations of Mathematics or MATH 235 Geometry - 4 credits
MATH 232 PHIL 293 Infinity, Undecidability, Non-computability - 4 credits
Total credit hours required for philosophy of mathematics minor majoring in philosophy – 16 credits

Required of mathematics majors

PHIL 310 Ancient Western Philosophy or PHIL 320 Modern Western Philosophy - 4 credits
PHIL 292 Formal Logic - 4 credits
PHIL 401 Topics in Contemporary Analytic Philosophy - 4 credits
MATH 232 PHIL 293 Infinity, Undecidability, Non-computability - 4 credits
Total credit hours required for philosophy of mathematics minor majoring in mathematics – 16 credits

Mathematics at Guilford

Why Mathematics at Guilford?

While many people associate mathematics with calculations and arithmetic, there is much more to math than simply crunching numbers. In its most general form, math is sometimes described as the science of patterns. Some of the patterns mathematicians explore include algorithms, sets, sequences, graphs, networks, functional relations, statistical data, and geometric and topological structures. Since the analysis and understanding of patterns is important in virtually every discipline, the ideas and methods of mathematics can be applied in almost any field. Sometimes mathematical analysis allows for the prediction of certain patterns (or at least of their likelihood). Other times, just as importantly, mathematics reveals that making a prediction with reasonable certainty is impossible.

Students who are well versed in math will be better prepared for employment and for graduate work in any field that deals with data analysis, quantitative reasoning, or logical deduction. Mathematics students will also be better able to understand recent advances in subjects where mathematical methods are routinely applied. Even in fields such as law and philosophy, where computational issues may not be emphasized, the use of logical thinking as required by mathematical proofs is a valuable skill.

Many majors at Guilford, including business administration, biology, chemistry, and physics, already require mathematics courses. However, the increasing use of mathematical methods and terminology in many fields, scientific and otherwise, is a great reason to study more than just the bare minimum of mathematics. Questions about infinity, higher dimensions, the limitations of computing, and the prediction of future events are just some of the topics up for grabs.

If you are a current or prospective student who wants to know more about the different math courses Guilford has to offer, please contact any of the mathematics faculty, and we’d be happy to tell you more.

Navigating the Mathematics Major

As with any course of study at Guilford, successfully majoring in mathematics involves a certain amount of planning. The courses a math major completes can be divided into three types:

The Calculus Sequence and Math 320/325

The only calculus course required for the major is Math 225 (Multivariable Calculus). However, this course is the third step in a typical calculus sequence, and so students will need to study two semesters’ worth of single-variable calculus to prepare for Math 225.

The set of courses students take before Math 225 depends on their background. Math 121 (Calculus I) is a typical entry point, but students who have already learned some calculus could potentially skip to Math 122 (Calculus II), or all the way to Math 225. This option is intended for students who are currently comfortable with the earlier courses; students who have taken calculus a long time ago are encouraged to retake the courses if they no longer remember the content.

Students who need a refresher on algebra, trigonometry, and exponential functions can choose to take Math 115 (Elementary Functions) before beginning the calculus sequence. Students who have covered the material in Calculus I and Calculus II but want to re-explore the material in more depth should consider Math 123 (Accelerated Calculus), offered every fall.

The math major also requires either Math 320 (Mathematical Physics) or Math 325 (Linear Algebra), each of which requires Multivariable Calculus as a prerequisite. For planning purposes, either of these courses can be thought of as a fourth step in the calculus sequence. Math 320 is typically offered in the fall, while Math 325 is typically offered in the spring.

Foundations of Mathematics and Upper-Level Courses

Math 231 (Foundations of Mathematics) is an introduction to proofs and abstract mathematical thinking, and in a sense it is a gateway to the upper-level courses of the mathematics department. This course is offered every spring, and potential math majors should strongly consider taking the course during the spring of their first or second year at Guilford.

Students must also take one upper-level course classified as theoretical, and one classified as applied. The three theoretical options are Math 335 (Topology), Math 430 (Algebraic Structures), and Math 435 (Real Analysis). Each of these courses requires Math 231 as a prerequisite. The three applied courses are Math 310 (Probability and Statistics), which requires Math 225; Math 412 (Discrete Mathematics II), which should be taken after Math 212; and Math 415, which requires Math 325. Any of these courses may be replaced by a 400-level seminar course; these seminars are occasionally arranged by faculty based on student interest.

Additional Electives

The mathematics major requires a minimum of 32 credits in courses numbered above 120; this includes three elective courses beyond the five courses specifically required. Students who take calculus courses at Guilford to prepare for Math 225 may satisfy one or two of these electives through Math 121, 122, and/or 123.

Other options include Math 212 (Discrete Mathematics I), Math 232 (Infinity, Undecidability, and Noncomputability), Math 235 (Geometry), additional upper-level courses, or seminars and independent studies.

Suggested Tracks

As is apparent from the descriptions above, the mathematics major offers a high level of flexibility. The decision of which courses to take can be made based on a student’s interest, schedule, and intended career path. Here are some suggested tracks:

  • Students primarily interested in theoretical mathematics, especially those planning to continue on to graduate study, should take all three of the upper-level theoretical courses (Topology, Algebraic Structures, and Real Analysis).
  • Students primarily interested in applying mathematics to non-mathematical areas should take Probability & Statistics and Linear Algebra, and perhaps consider arranging a seminar on a topic related to their area of interest.
  • Students primarily interested in computer-oriented mathematics should take Discrete Mathematics I, Discrete Mathematics II, and Linear Algebra. Numerical Analysis may also be a good choice.
  • Students preparing for secondary education are encouraged to take Geometry, Probability & Statistics, and Algebraic Structures.

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