Introduction to Actuarial and Financial Mathematical Methods

1st Edition

Authors: Stephen Garrett
Hardcover ISBN: 9780128001561
eBook ISBN: 9780128004913
Imprint: Academic Press
Published Date: 7th April 2015
Page Count: 624
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This self-contained module for independent study covers the subjects most often needed by non-mathematics graduates, such as fundamental calculus, linear algebra, probability, and basic numerical methods. The easily-understandable text of Introduction to Actuarial and Mathematical Methods features examples, motivations, and lots of practice from a large number of end-of-chapter questions. For readers with diverse backgrounds entering programs of the Institute and Faculty of Actuaries, the Society of Actuaries, and the CFA Institute, Introduction to Actuarial and Mathematical Methods can provide a consistency of mathematical knowledge from the outset.

Key Features

  • Presents a self-study mathematics refresher course for the first two years of an actuarial program
  • Features examples, motivations, and practice problems from a large number of end-of-chapter questions designed to promote independent thinking and the application of mathematical ideas
  • Practitioner friendly rather than academic
  • Ideal for self-study and as a reference source for readers with diverse backgrounds entering programs of the Institute and Faculty of Actuaries, the Society of Actuaries, and the CFA Institute


Actuarial and finance students worldwide who need to learn or revisit fundamental applied mathematical tools and techniques

Table of Contents

  • Dedication
  • Preface
  • Part 1: Fundamental Mathematics

    • Chapter 1: Mathematical Language

      • Abstract
      • 1.1 Common mathematical notation
      • 1.2 More advanced notation
      • 1.3 Algebraic expressions
      • 1.4 Questions
    • Chapter 2: Exploring Functions

      • Abstract
      • 2.1 General Properties and Methods
      • 2.2 Combining Functions
      • 2.3 Common Classes of Functions
      • 2.4 Inverse Functions
      • 2.5 Actuarial Application: The Time Value of Money
      • 2.6 Questions
    • Chapter 3: Differential Calculus

      • Abstract
      • 3.1 Continuity
      • 3.2 Derivatives
      • 3.3 Derivatives of More Complicated Functions
      • 3.4 Algebraic Derivatives on Your Computer
      • 3.5 Actuarial Application: The Force of Interest
      • 3.6 Questions
    • Chapter 4: Differential Calculus II

      • Abstract
      • 4.1 An Introduction to Smoothness
      • 4.2 Higher-Order Derivatives
      • 4.3 Stationary and Turning Points
      • 4.4 Higher-Order Derivatives and Stationary Points on Your Computer
      • 4.5 Actuarial Application: Approximating Price Sensitivities
      • 4.6 Questions
    • Chapter 5: Sequences and Series

      • Abstract
      • 5.1 Sequences
      • 5.2 Series and Summations
      • 5.3 Evaluating Summations
      • 5.4 Taylor and Maclaurin Series
      • 5.5 Series and Summations on Your Computer
      • 5.6 Actuarial Application: Annuities
      • 5.7 Questions
    • Chapter 6: Integral Calculus I

      • Abstract
      • 6.1 Indefinite Integrals of Basic Functions
      • 6.2 Change of Variables Approach
      • 6.3 Indefinite Integrals of Products of Functions
      • 6.4 Indefinite Integrals of Rational Functions
      • 6.5 Indefinite Integrals on Your Computer
      • 6.6 Questions
    • Chapter 7: Integral Calculus II

      • Abstract
      • 7.


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© Academic Press 2015
Academic Press
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About the Author

Stephen Garrett

Prof. Stephen Garrett is Professor of Mathematical Sciences at the University of Leicester in the UK. He is currently Head of Actuarial Science in the Department of Mathematics, and also Head of the Thermofluids Research Group in the Department of Engineering. These two distinct responsibilities reflect his background and achievements in both actuarial science education and fluid mechanics research. Stephen is a Fellow of the Royal Aeronautical Society, the highest grade attainable in the world's foremost aerospace institution.

Affiliations and Expertise

Professor of Mathematical Sciences, University of Leicester, UK


"This book is an ideal introduction to the mathematical background required for students who wish to embark on an actuarial or financial career. It will be especially useful to students who have not taken a mathematical degree. The extensive examples throughout the book show how the mathematics can be used in practice and enable students to gain a thorough understanding of the material." --John Millett, University of Kent