Prerequisites & Distribution: Students with credit for Math. 103 can elect Math. 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. (4). (MSA). (QR/1).
Credits: (4).
Course Homepage: No Homepage Submitted.
Math 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who complete 105 are fully prepared for Math 115. This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. Math 110 is a condensed half-term version of the same material offered as a self-study course through the Math Lab.
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Prerequisites & Distribution: Math. 115. Credit is granted for only one course from among Math. 116, 119, 156, 176, 186, and 296. (4). (MSA). (BS). (QR/1).
Credits: (4).
Course Homepage: No Homepage Submitted.
See Math 115 for a general description of the sequence Math 115-116-215.
Topics include the indefinite integral, techniques of integration, introduction to differential equations, infinite series. Math 186 is a somewhat more theoretical course which covers much of the same material. Math 215 is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking Math 285.
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Prerequisites & Distribution: (1). (Excl). (BS). May be repeated for credit with permission.
Credits: (1).
Course Homepage: No Homepage Submitted.
One of the best ways to develop mathematical abilities is by solving problems using a variety of methods. Familiarity with numerous methods is a great asset to the developing student of mathematics. Methods learned in attacking a specific problem frequently find application in many other areas of mathematics. In many instances an interest in and appreciation of mathematics is better developed by solving problems than by hearing formal lectures on specific topics. The student has an opportunity to participate more actively in his/her education and development. This course is intended for superior students who have exhibited both ability and interest in doing mathematics, but it is not restricted to honors students. This course is excellent preparation for the Putnam exam. Students and one or more faculty and graduate student assistants will meet in small groups to explore problems in many different areas of mathematics. Problems will be selected according to the interests and background of the students.
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Prerequisites & Distribution: Math. 412 or 451 or equivalent experience with abstract mathematics. (3). (Excl). (BS).
Credits: (3).
Course Homepage: http://www.math.lsa.umich.edu/~selinger/481/
Course Description: Logic is the study of the formal principles
of reasoning. In this course, we will study symbolic logic. We
will introduce the formal languages of propositional and first-order
logic, and we will learn how to formalize the notions of truth
and proof. Logic is unlike any other branch of mathematics, in
that we do not just prove things, but we reason about
properties of proofs. For this reason, logic has sometimes been called
meta-mathematics. On the other hand, the study of modern formal
logic uses some of the same methods and techniques that are used in
other branches of mathematics, and thus logic can also be regarded as
a mathematical discipline.
Topics: In the first part of the course, we will introduce the
notion of a formal language. We will study the propositional
connectives, tautologies, and tautological consequences. The heart of
the course is the study of first order predicate logic and its models.
We will study formal proofs, establish soundness and completeness
theorems, and explore some of their applications. We will see how to
formalize elementary number theory. By the end of the course we
should be able to state and understand Gödel's First
Incompleteness Theorem.
Prerequisites: The official prerequisite, "Math 412 or 451 or
equivalent experience with abstract mathematics," means that students
should be comfortable with writing mathematical proofs. No specific
knowledge of formal logic will be presupposed.
Course Work: There will be two in-class (1 hour) midterms and one
final exam. There will also be regular homework assignments, which
will be collected in class.
Grading: Grades will be based on exam performance. Each midterm
counts 30% and the final 50%. Out of these 110%, the lowest 10% will
be dropped. In borderline cases, homework will be the tie-breaker.
Textbook: Herbert B. Enderton. A Mathematical Introduction
to Logic. Academic Press.
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Prerequisites & Distribution: Math. 425. (3). (Excl). (BS).
Credits: (3).
Course Homepage: http://www.math.lsa.umich.edu/~conlon/math523/index.html
Prerequisites: A solid background in probability theory at the 400
level, math 425 or equivalent.
Required Texts: Actuarial Mathematics by Bowers, Gerber,
Hickman, Jones and Nesbitt, Society of Actuaries, 1986.
Introduction to Credibility Theory by Herzog, Actex, 1994.
Background and Goals: Risk management is of major concern to
all financial institutions and is an active area of modern finance.
This course is relevant for students with interests in finance, risk
management, or insurance. It provides background for the
professional exams in Risk Theory offered by the Society of
Actuaries and the Casualty Actuary Society.
Content: (a) Utility theory, stop-loss insurance, theory of
aggregate claims, compound Poisson claims model, estimating
the probability of ruin, reinsurance schemes and their implications
for profit and risk.
(b) Credibility theory, classical theory for independent events, least
squares theory for correlated events, examples of random
variables where the least squares theory is exact.
Grading: The grade for the course will be determined from
performances on 8 quizzes, a midterm and a final exam. There
will be 8 homework assignments. Each quiz will consist of a
slightly modified homework problem.
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This page was created at 11:39 AM on Wed, Sep 29, 1999.