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.
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.
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.
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.