Objectives

This course aims at refreshing mathematical notions and techniques and developing complements which will be useful for applications in the fields of actuarial science and finance. The goal is to provide a common base of general techniques of differential and integral calculus and of linear algebra used in the other courses. Many examples drawn for actuarial science will illustrate the necessity for future actuaries to master these skills.

Contents

Differential and Integral Calculus

• Sets of Numbers, Sequences, Infinite Series
• Functions, Continuity, Differentiation
• Integration
• Partial Derivatives, Repeated Integrals
• Complex Numbers, Laplace/Fourier Transforms

Linear algebra

• Linear Equation Systems
• Vector Spaces
• Eigenvalues and Eigenvectors
• Decompositions of Matrices

References

Lay, David C., Steven R. Lay, Judi J. McDonald, "Linear Algebra and Its Applications" (5th ed), Pearson, 2016

Ross, K.A., "Elementary Analysis: The Theory of Calculus", Springer, 2nd edition, 2013.

Rudin, W., "Real and complex analysis", McGraw-Hill, 3rd edition, 1987.

Rudin, W., "Principles of mathematical analysis", McGraw-Hill, 3rd edition, 1976.

Riley, K.F., Hobson, M.P., Bence, S.J., "Mathematical methods for physics and engineering", Cambridge University Press, 3rd edition, 2006.

Evaluation

First attempt

Exam:

Written 3h00 hours

Documentation:

Allowed with restrictions

Calculator:

Allowed with restrictions

Evaluation:

Midterm: 30%

Final: 70% == 50% (Linear Algebra) + 20% (Calculus/Analysis)

Documentation: A single sheet (A4) hand-written (by the student) on both sides.

Calculator: Restriction on calculator (simple scientific calculator, non-programmable).

Retake

Exam:

Written 3h00 hours

Documentation:

Allowed

Calculator:

Allowed with restrictions

Evaluation:

Retake: 100% == 50% (Linear Algebra) + 50% (Calculus/Analysis)

Documentation: A single sheet (A4) hand-written (by the student) on both sides.

Calculator: Restriction on calculator (simple scientific calculator, non-programmable).