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Course 1
Mathematical Foundations of
Actuarial Science
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This course is jointly administered by the SOA and CAS.
The examination for this course consists of four hours of multiplechoice questions and is identical to CAS Exam 1.
The purpose of this course is to develop a knowledge of the
fundamental mathematical tools for quantitatively assessing risk.
The application of these tools to problems encountered in actuarial
science is emphasized. A thorough command of calculus and
probability topics is assumed. Additionally, a very basic knowledge
of insurance and risk management is assumed.
The tools emphasized are:
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Limits, series, sequences and functions;
Derivatives of single and multivariate functions (maximums,
minimums, constrained maximums and minimums, rate of
change);
Integrals of single and multivariate functions, simple
differential equations;
Parameterized curves;
General probability (set functions, basic axioms,
independence);
Bayes' Theorem;
Univariate probability distributions (probabilities, moments,
variance, mode, percentiles, transformations);
Multivariate probability distributions (Central Limit Theorem;
joint, conditional and marginal distributions-probabilities,
moments, variance, covariance).
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A table of values for the normal distribution will be included with the
examination booklet.
Suggested Texts
The texts listed below are considered representative of the many
texts used by colleges and universities in Canada and the US to
cover material on which the candidate may be examined. Earlier or
later editions of the listed texts contain essentially the same
material and should be adequate for review purposes. In addition
there are study notes for this course. The candidate is expected to
be familiar with the concepts introduced in the study notes.
Calculus
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Calculus (Seventh Edition), 2002, by Larson, R.E., Hostetler,
R.P. and Edwards, B.H.
Calculus: Concepts and Contexts (Second Edition), 2001, by
Stewart, J.
Calculus: Graphic, Numerical and Algebraic, 1999, by
Finney, R.L., Demana, F.D.
and Waits, B.K.
Calculus: Late Transcendentals (Seventh Edition), 2001, by
Anton, H., Bivens, I.
and Davis, S.
Calculus with Analytic Geometry (Fifth Edition), 1997, by
Edwards, C.H. and Penney, D.E.
Probability
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A First Course in Probability (Sixth Edition), 2001, by Ross,
S.M., Chapters 1-8.
Fundamentals of Probability (Second Edition), 1999, by
Ghahramani, S., Chapters 1-10.
Probability for Risk Management, 1999, by Hassett, M. and
Stewart, D., Chapters 1-11.
Probability and Statistical Inference (Sixth Edition), 2001, by
Hogg, R.V. and Tanis, E.A.,
Chapters 1-6.
Probability: The Science of Uncertainty with Applications to
Investments, Insurance and Engineering 2001, by Bean,
M.A., Chapters 1-9.
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Study Notes
Hard copies may be purchased by using the Study Note and
Published Reference order form in the back of the printed
catalog or on the "Study Notes/Information" Web page.
Code
Title
1-11-02# Course 1 Introductory Study Note
Tables for the Course 1
1-12-00
1-10-01
1-12-01
Examination
November 2000 Course/Exam 1
May 2001 Course/Exam 1
November 2001 Course/Exam 1
1-21-00
Risk and Insurance
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Study Note Courses 1-5 | Fall 2002 Catalog | Education and
Examinations