Students in the College of Engineering and Applied Science are required to take a calculus sequence and for many of the majors additional more advanced mathematics courses. Because the calculus courses are prerequisites for many courses taken by engineering students, these students should begin calculus during their first semester.
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.
The main calculus sequence for engineering students is MATH 21, 22, 23. There are four possible variations on this sequence:
Advanced placement
Honors calculus
A slower paced version of calculus with some precalculus review
Extensive preliminary precalculus review
All students planning on taking a calculus course must take a readiness test. Information on the readiness test and the various options will be given below (also see the Readiness Test page). Students interested in other mathematics courses should consult the catalog or a member of the department.
Students who have advanced placement for all three calculus courses should consult the catalog to determine which other mathematics courses are required for their prospective major.
Readiness Tests:
Except
as noted below in the Advanced Placement section, all students who plan
to take Math 21 in the fall semester must take a calculus readiness exam
during the summer preregistration process or in August during orientation.
These are tests on precalculus mathematics, such as algebra, graphing,
functions, and trigonometry. The purpose of the readiness exam is to ensure
that students are appropriately placed and to identify students who need
additional preparation before taking the required calculus courses. A sample
readiness exam is enclosed.
Students whose scores on the calculus readiness exam indicate that they lack sufficient preparation must take Math 75, 76.In the unlikely event of an extremely low score
on the calculus readiness exam, a student must take Math 0 followed by Math 21 (see descriptions below).
Advanced Placement (AP Credits):
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, or 31 now, and if the AP exam scores warrant credit, the appropriate adjustments can be made later. Advanced placement 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
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; in this case, you need not take the
calculus readiness exam.Similarly,
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 courses do not provide adequate preparation
for calculus at Lehigh.
Depending
on demand, the Department of Mathematics may offer anticipatory exams for
Math 21, 22 and 23 during the orientation period.
Introductory Calculus Courses:
There are two main calculus sequences - MATH 31,32,33: Honors Calculus and MATH 21,22,23: Calculus.There is a third calculus sequence, MATH 51,52: Survey of Calculus but this does not meet requirements in the College of Engineering and Applied Science. Thus, the course numbers do not follow the level of difficulty of the classes. The 20's sequence is a systematic development of calculus. As an Honors sequence, the 30’s sequence presents essentially the same material but in even greater depth and with more attention to rigor and proof.MATH 75,76: Calculus I, parts A and B together substitute for MATH 21, developing the same material at a somewhat slower pace, over two semester-long 2 credit courses. In terms of prerequisites the 30’s, 20’s order is followed. For example, a prerequisite of MATH 21 would be satisfied by MATH 31.
Calculus Courses:
Math 75, 76: Calculus I, parts A and B:
These are 2 credit courses that together replace MATH 21. These two courses constitute a year long sequence (which must be started in the fall) that substitutes for MATH 21. The slower pace and additional precalculus material is intended to allow students who need more preparation to master the material of MATH 21. Both courses have 2 lectures and one meeting in a small group with a graduate student.
MATH 21, 22, 23: Calculus I, II, III:
These are 4 credit courses required for engineering, mathematics, physics and chemistry and some are required for business.They are typically taken by students in these programs as well as by other students with a strong background and an interest in a rigorous calculus sequence. Each week there are 3 lectures and one meeting in a small group with a graduate student. Each of these courses is offered in both semesters each year. . Students who start with Math 21 and find themselves struggling can switch to Math 75 as long as they do so in a timely fashion.
MATH 31, 32, 33: Honors Calculus I, II, III:
These cover the same material as MATH 21, 22, 23 but with more depth and rigor. They are aimed at students with a high aptitude (an Sat math score of over 700 is expected but not required) and motivation in mathematics. They are particularly aimed at students intending to major in mathematics and students with a strong interest in rigorous mathematics who plan on other majors. Honors classes typically have less than 15 students. For MATH 31, 32, 33 each week students meet 4 times with a professor, usually involving lectures and problem solving sessions. MATH 31 and 33 are offered in the fall and MATH 32 is offered in the spring.