An Introduction to the Mathematics of Money
Saving and Investing
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Beschreibung
This is an undergraduate textbook on the basic aspects of personal savings and investing with a balanced mix of mathematical rigor and economic intuition. It uses routine financial calculations as the motivation and basis for tools of elementary real analysis rather than taking the latter as given. Proofs using induction, recurrence relations and proofs by contradiction are covered. Inequalities such as the Arithmetic-Geometric Mean Inequality and the Cauchy-Schwarz Inequality are used. Basic topics in probability and statistics are presented. The student is introduced to elements of saving and investing that are of life-long practical use. These include savings and checking accounts, certificates of deposit, student loans, credit cards, mortgages, buying and selling bonds, and buying and selling stocks.
The book is self contained and accessible. The authors follow a systematic pattern for each chapter including a variety of examples and exercises ensuring that the student deals with realities, rather than theoretical idealizations. It is suitable for courses in mathematics, investing, banking, financial engineering, and related topics.
This book is an introduction to the mathematics of finance. Part I focuses on analysis of deterministic cash flows, such as those generated by risk-free instruments such as bonds and annuities. Part II analyzes risky securities, such as stocks and options. This book is suitable for undergraduates in mathematics, economics and business programmes. It contains examples and exercises throughout. The book uses investing as a vehicle to introduce ideas, techniques and applications that might not be encountered in other mathematics courses. These include proofs by induction, recurrence relations, inequalities (in particular, the Arithmetic-Geometric Mean inequality and the Cauchy-Schwarz inequality), and the elements of probability and statistics. The book introduces the reader to principles of investing that will be of life-long practical use. This book targets students at the sophomore/junior level, without assuming a background or any experience in investing.
Many illustrations included throughout the text Exercises at the end of each chapter An only undergraduate text providing an introduction to the mathematics of savings Includes supplementary material: sn.pub/extras
Autor*in
David Lovelock
Themen in »An Introduction to the Mathematics of Money«
Arithmetic Calculation banking economics finance inflation mathematics pricing proof statistics stock market quantitative finance
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From the reviews:
"This book is written for students without assuming a background or any experience in investing. A basic knowledge in real analysis is necessary. The student is introduced to elements of saving and investing that are of lifelong practical use. These includes saving, checking accounts, certificates of deposit, student loan, credit cards, mortgages, buying and selling bonds of stocks. The authors follow a systematic pattern with a variety of examples and exercises. … suitable for fundamental courses in mathematics, investing, banking, financial engineering, and related topics." (Klaus Ehemann, Zentralblatt MATH, Vol. 1114 (16), 2007)
"This book is designed to serve as an undergraduate text on the fundamentals of personal savings and investing. … The book includes an appendix that covers basic concepts and techniques in probability and mathematical statistics. … follows a different philosophy; it allows the results and examples to speak for themselves. … it serves as a valuable resource for attaining savings, investment, and retirement goals." (Joseph Cavanaugh, The American Statistician, Vol. 62 (2), May, 2008)
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