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An Introduction to the Mathematics of Money: Saving and Investing

Год выпуска: 2006
Автор: David Lovelock and Marilou Mendel and Arthur L. Wright

Synopses & Reviews

Publisher Comments

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.

Review

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)

Synopsis

This book is an introduction to the mathematics of finance. Part I focuses on analysis of deterministic cash flows, such as those generated by riskless bonds and annuities. Part II focuses on the analysis of 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. This book uses investing as a vehicle to introduce ideas, techniques and applications that might not be encountered 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 the elements of investing that are of life-long practical use. This book targets students at the sophomore/junior level, without assuming a background or any experience in investing.

Synopsis

Introduction Some people distinguish between savings and investments, where savings are monies placed in relatively risk-free accounts with modest rewards, and where investments involve more risk and the potential for greater rewards. In this book we do not distinguish between these ideas. We treat them both under the umbrella of investing. In general, income falls into two categories: earned income which is the income derived from your everyday job andunearnedincome which is income derived from investing. You attend college to strengthen your prospects for earned income, so why do you need to worry about unearned income, namely, investment income? There are many reasons to invest and to learn about investing. Perhaps the primary one is to take charge of your own ?nancial future. You need money for short-term goals (such as living expenses, emergencies) and for long-term goals (such as buying a car, buying a house, educating children, paying catastrophic medical bills, funding retirement). Investing involvesborrowingandlending, andbuyingandselling. borrowing and lending. When you put money into a bank savings account, youarelendingyourmoneyandthebankisborrowingit.Youcan lend money to a bank, a business, a government, or a person. In exchange forthis, theborrowerpromisestopayyouinterestandtoreturnyourinitial investment at a future date. Why would the borrower do this? Because the borrower anticipates using this money in a way that earns more than the interest promised to you. Examples of borrowing and lending are savings accounts, certi?cates of deposits, money-market accounts, and bonds."

Synopsis

This book uses investing as a vehicle to introduce students at the sophomore and junior levels to mathematical ideas, techniques, and applications which may not be covered in other classes. Proofs using induction, recurrence relations and proofs by contradiction are covered. Inequalities such as the Arithmetic-Geometric 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 credit cards, student loans, savings and checking accounts, certificates of deposit, mortgage payments, buying and selling bonds, and buying and selling stocks. There are novel approaches to several of these topics, and new examples and exercises appear throughout the book.

Synopsis

This introduction to the mathematics of finance is suitable for undergraduates in mathematics, economics and business programmes. Assuming no background or experience in investing, the book introduces the reader to principles of investing that will be of life-long practical use.

Table of Contents

Preface.- Interest - Simple.- Interest - Compound.- Inflation and Taxes.- Annuities.- Loans and Risks.- Amortization.- Credit Cards.- Bonds.- Stocks and Stock Markets.- Stock Market Indexes, Pricing, and Risk.- Options.- Appendix: Induction, Recurrence Relations, Inequalities.- Appendix: Statistics.- Answers.- References.- Index.



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