Mathematics (MATH) Chair
: A. Robertson DEPARTMENT SITE
Students study mathematics for many reasons: preparation for a career, use in another field, or the beauty of the subject itself. Colgate math majors go on to careers in mathematics, finance, medicine, law, teaching, business administration and areas of industry and education with a mathematics and science orientation. Non-majors find mathematics courses interesting and useful too. Mathematics uses a universal language that assists precise expression, logical reasoning and expression of abstract concepts. Mathematics is also an art form, to be studied for its own intrinsic beauty.
Typical entry-level mathematics courses include the Calculus sequence (MATH 161, 162,
). All mathematics courses are open to qualified students. Entering first-year students who have successfully completed at least three years of secondary school mathematics, including trigonometry, should be adequately prepared for MATH 161
. Students who have studied calculus in secondary school are typically ready to enter MATH 162
Please consult the list of topics under MATH 161, 162, and 163
, and use it as a guide for placement. If you have been exposed to calculus in high school, whether you have received AP credit or not, you should carefully consider your placement within the calculus sequence. You need to ensure you are sufficiently challenged to stay engaged and at the same time, not struggling to catch up. The department does not force students to enroll in any particular course; rather you must place yourself based on your background and comfort with the material.
Anyone who has had a full year of study in calculus is strongly encouraged to register for MATH 162
. Anyone who has completed a course preparing for the AP Calculus BC exam should enroll in MATH 163
. Anyone who has completed a course preparing for the AP Calculus AB exam can enroll in MATH 162
. Consult the list of topics under MATH 161, 162
, and 163
for more information. For borderline cases, enrolling in a higher-level course is generally the better long-term decision. Students are allowed to drop back from MATH 162
to MATH 161
at any time during the first three weeks of classes. Members of the mathematics faculty will be available during Orientation and the first week of classes to advise students about placement within the calculus sequence and the mathematics program more generally.
Colgate course credit is awarded to students receiving a score of 4 or 5 on the AP Calculus AB exam; a score of 3, 4, or 5 on the AP Calculus BC exam; or a score of 4 or 5 on the AP Statistics exam. Students receiving a score of 4 or 5 on the AP Calculus AB exam will receive credit for MATH 161
. Students receiving a score of 3 on the AP Calculus BC exam will receive credit for MATH 161
. Students receiving a score of 4 or 5 on the AP Calculus BC exam will receive credit for MATH 161
and MATH 162
. Students receiving a score of 4 or 5 on the AP Statistics exam will receive credit for MATH 105
. Please note, however, if a student enrolls in a course or drops back to a lower level course for which he or she has received AP credit, the AP credit will be excluded from the student’s academic record and the course will be noted on the transcript as a repeated course. There are no other circumstances under which a student will receive mathematics credit at Colgate University for a course taken in high school.
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MATH 105, Introduction to Statistics
An introduction to the basic concepts of statistics. Topics include experimental design, descriptive statistics, correlation, regression, basic probability, mean tendencies, the central limit theorem, point estimation with errors, hypothesis testing for means, proportions, paired data, and the chi-squared test for independence. Emphasis is on statistical reasoning rather than computation, although computation is done via software.
MATH 161, Calculus I
An introduction to the basic concepts of differential and integral calculus including limits and continuity; differentiation of algebraic, trigonometric, exponential, and logarithmic functions; applications of the derivative to curve sketching, related rates, and maximum-minimum problems; Riemann sums and the definite integral; and the fundamental theorem of calculus.
MATH 162, Calculus II
A continuation of the study of calculus begun in MATH 161. Topics covered include the calculus of inverse trigonometric functions, techniques of integration, improper integrals, l'Hôpital's rule and indeterminate forms, applications of integration, and Taylor series.
MATH 163, Calculus III
The content from MATH 162 and MATH 163 is extended to several variables. Among the topics considered are surfaces in three-dimensional space, partial derivatives, maxima and minima, and multiple integrals.