Every Lehigh student must meet a three–credit mathematics requirement. Ordinarily, students meet this requirement with a mathematics course, although certain philosophy and computer science courses are also designated for this requirement.

     Students need to carefully consider which mathematics courses they should take. There are a number of factors to bear in mind, notably your intellectual interests as well as the requirements of your prospective major. Some degree programs, particularly in the natural sciences, computer science, architecture, cognitive science, and economics, require specific mathematics courses, so students majoring in those programs meet the mathematics requirement by completing their major requirements. In some cases, the required courses are calculus courses (Math 21 or 51) that are prerequisites for courses in the major, so it may be important to take calculus right away. For example, if you don’t have AP credit for Math 21, you should take Math 21 (or 31 or 51) concurrently with Phy 11. In cases like that, a delay in taking mathematics will delay progress in your major. The social science disciplines strongly encourage students in their major programs to take a statistics course like Math 12, which also meets the mathematics requirement. The humanities degree programs, other than Architecture, require no particular mathematics course, so students majoring in those programs can select any three credits of mathematics coursework to meet the requirement.
     Students should consult the Course Catalog to determine mathematics courses that are required and recommended by different degree programs. If you know that you want to follow a curriculum that requires calculus, you should begin right away. If you think you might want to follow a curriculum that requires calculus, you should seriously consider beginning right away. If you know or think you want to follow a curriculum that requires statistics, you should seriously consider taking it as early as you can. Experience has shown that it is unwise to let too much time elapse between your last high school mathematics course and your first mathematics course at Lehigh. The loss of ‘momentum’ will be particularly difficult if you decide to study calculus.
     If you can unequivocally say that you have no interest in any curriculum that requires calculus, stop and consider any goals you might have besides meeting the requirements of a specific major. Graduate and professional schools may require more mathematics than your major requires. Phi Beta Kappa requires calculus. Calculus is, indeed, one of humankind’s great intellectual achievements, and it can play a definite role in any student’s liberal arts education (which is why Phi Beta Kappa requires it!). If you can still unequivocally say that you don’t need calculus, you can wait to take the course that will meet the mathematics requirement. Explore your curricular options, and once you know what you will do for a major, you can decide whether you should take statistics or another non–calculus option. Keep in mind that putting unnecessary distance between your high school mathematics and your Lehigh mathematics may offset any advantages of delaying mathematics.

     Advanced placement credit in mathematics is usually awarded for either Math 12 (Basic Statistics) or Math 21 (Calculus I) or Math 21 and 22 (Calculus I and II), as appropriate depending on the exam and the score. Such advanced placement satisfies the mathematics distribution requirement. Advanced placement and calculus readiness tests will be discussed below  in the section after Introductory Calculus Courses (also see the AP Credits page).

Non–calculus introductory courses
Math 5 is well suited to students majoring in the humanities. The math content is ‘real,’ and students should expect to work at ‘doing math.’

Math 5, Introduction to Mathematical Thought (3 credits) spring
This course introduces students to the meaning, content, and methods of mathematical thought. It leans more toward the philosophical underpinnings of mathematics than applications. Topics used for illustration will vary. Students do not need strong high school math background.

Math 12, Basic Statistics (4 credits) fall and spring
This course provides a foundation for the statistical description and analysis of data, which are fundamental issues in the social sciences. Students in the natural sciences also benefit from studying statistics, although calculus might be a higher priority early.

Math 43, Survey of Linear Algebra (3 credits) fall
This course covers matrices and is required for certain Biological Sciences degree programs.

Introductory Calculus Courses
With three different calculus sequences, the Mathematics Department is able to tailor its offerings to students with different preparations and needs for studying calculus.

     § the 20s sequence
               Math 21, Calculus I (4 credits each) fall and spring
               Math 22, Calculus II (4 credits each) fall and spring
               Math 23, Calculus III (4 credits each) fall and spring
                 also Math 75 and 76, Calculus I, parts A and B, substitute for Math 21
The 20s sequence (12 credits) is required of all engineering students as well as majors in Mathematics, Computer Science, and many natural science programs. The College of Business and Economics requires Math 21 in its curriculum. The three semesters cover single– and multiple–variable calculus and introduce differential equations. Math 75 and 76 (2 credits each) divide the material of Math 21 into two parts for students whose degree programs require Math 21 but who are not prepared to go directly into Math 21. Successful completion of Math 21 or Math 76 is a prerequisite for Math 22. Students who start with Math 21 and find themselves struggling can switch to Math 75 or Math 51 as long as they do so in a timely fashion.

     § the 30s sequence
               Math 31, Honors Calculus I (4 credits) fall
               Math 32, Honors Calculus II (4 credits) spring
               Math 33, Honors Calculus III (4 credits) fall
The 30s sequence  (12 credits) is the most in–depth and rigorous sequence and requires the most student effort. It covers the same material as the 20s sequence and, therefore, meets any stated requirement for the 20s sequence. Classes are small, and the ‘Honors’ designation in the course title records the student’s high aptitude and motivation for mathematics.

     § the 50s sequence
              Math 51, Survey of Calculus I (4 credits) fall
              Math 52, Survey of Calculus II (3 credits) spring
The 50s sequence covers much of the material covered in 21 and 22 but not in as much depth, allowing the material to be completed with fewer credits (totaling 7 credits). This sequence is suited for Architecture and some natural science programs. Math 21 is usually an acceptable substitute for Math 51 but not the reverse, and Math 21 is an acceptable prerequisite for 52 but 51 is not a prerequisite for 22; students with strong mathematics backgrounds might consider starting with the 20s sequence if they have any question about which sequence best suits their curriculum.

There is a big difference between calculus study at Lehigh and calculus at most high schools. A solid high–school precalculus course is necessary background for calculus at Lehigh. Students need a strong foundation in functions (forms, graphs, roots) and trigonometry to really thrive in calculus. Most students who take calculus in high school are accustomed to using a graphing calculator. Calculators are not permitted in Lehigh calculus classes. Lehigh has very high standards, and calculus students are expected to learn calculus without relying on calculators. Many students find a summer course in calculus at a local community college to be helpful in bridging from high school mathematics to Lehigh calculus.

Advanced Placement for Calculus
Students who score 4 or 5 in the AB advanced placement exam may receive 4 credits for Math 21 and those who score 4 or 5 on the BC advanced placement exam may receive 8 credits for Math 21 and 22. Students should preregister for Math 21, 31, or 51 now, and if the AP exam scores warrant credit, the appropriate adjustments can be made later. Advanced placement credit and course credit is also granted for successful completion of approved college courses taken during high school. Approval is granted on a case-by-case basis and depends on submission of detailed information as to course content.

We often recommend that students consider beginning Lehigh calculus a semester below their advanced placement. If you have credit for Math 21 and are eligible for Math 22, consider taking Math 21; if you have credit for Math 21 and Math 22 and are eligible for Math 23, consider taking Math 22. You will relinquish some or all of your AP credit, but experience has shown that many AP course do not provide adequate preparation for calculus at Lehigh. Depending on demand, the Department of Mathematics may offer anticipatory exams for Math 51, 21, 22 and 23 during the orientation period.

Calculus Readiness Assessment
All students who plan to take Math 51 or Math 21 in the fall semester must take a calculus readiness assessment during the summer preregistration process. The assessment probes the student's background in precalculus mathematics, such as algebra, graphing, functions, and trigonometry. The purpose of the readiness assessment is to ensure that students are appropriately placed and to identify students who need additional preparation before taking the calculus course their intended majors require. A sample readiness assessment is enclosed.

Students whose scores on the Math 51 readiness assessment indicate that they lack sufficient preparation must take Math 0 (see description below) before taking Math 51.

Students whose scores on the Math 21 readiness assessment indicate that they lack sufficient preparation can take Math 75, 76 or Math 0 (see descriptions below).

Math 0, Preparation for Calculus (2 credits) fall
This course is for students who need more preparation before moving on to calculus, as evidenced by low scores on the readiness exam. The 2 credits do not count toward the total number of credits required for graduation, but the grade does count in the student’s GPA. Students taking Math 0 must pass with a grade of C– before taking Math 51 or 21.