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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.
- Sales Rank: #659679 in eBooks
- Published on: 2007-04-05
- Released on: 2007-04-05
- Format: Kindle eBook
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)
From the Back Cover
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.
Most helpful customer reviews
5 of 6 people found the following review helpful.
Good introduction to the mathematics of finance
By William S Rea
I taught a second year course in finance using this book as the basis for
the course. I covered all the chapters expect the last one on options.
I prepared material on options for the class, it was only because
the teaching term was cut short by the devastation caused by the earthquake
that we did not get to it.
In recent decades finance has beome much more mathematical. There are
a lot of very good books on the market on the advanced mathematics
required for quantitative analysis and risk management. When you are
looking for an introductory book which is suitable for a first course
in finance (we do not offer any finance courses at the first year level),
but which is quite mathematical in approach, the market becomes quite limited.
This is one book on offer and does a good job provided you are clear about
what you are trying to achieve by using it.
The book was written for the American market and the authors state it
is suitable for the sophomore or junior level (2nd or 3rd year
undergraduate in the US). I believe that is a fair assessment of the
level of the book.
The book has eleven chapters and two appendices.
The first eight chapters are devoted to topics
which could form the basis of an introduction to the mathematics of
fixed income. These eight chapters cover simple and compound
interest, inflation and taxation, annuities, loans, amortization,
credit cards and bonds. The bonds are, of course, the most plain
vanilla non-callable and zero coupon bonds. There some excellent
sections in these chapters. For example, most courses, if they mention
it at all, do not go into the problem that the internal rate of return (IRR)
may not be unique. This book gives a good account of the problem
and through its two theorems on the uniqueness of the IRR give the
student a clear idea of when an IRR will and will not be unique.
The chapter on bonds was also very good, it covers some aspects of the
modified duration which I've not seen in any other text.
These chapters also do have some limitations. In the chapter on annuities,
growing annuities and growing perpetuities were not covered so I added
material from Zipf's book, Fixed Income Mathematics, to the course to cover
these topics.
Chapters 9 and 10 are devoted to the stock market and chapter 11 is on
options. These are rather short but within the time constraints of
teaching the course in a single semester there is little room for
extra material. I found the account of the capital assest pricing
model (CAPM) to be weak and I will probably replace this with material
from another source when I next teach the course.
The final chapter is on options and even has an elementary derivation
of the Black-Scholes pricing model.
The two appendices are on some background mathematics and statistics
which probably adequately prepared students will have met before.
The mathematics section deals with proof by induction and
recurrence relations, and some inequalities such as the Cauchy-Schwarz
and the arthimetic-geometric mean inequality. The appendix on statistics
is a bit more comprehensive but, again, a student who has passed a
first year level course in statistics should have covered all this
material. It is there for completeness so if a student needs to
look up a result they may be able to find it in one of the appendices
rather than having to head off to a more comprehensive math or stats text.
Each chapter has a number of exercises. These are divided into what the
author's call ``walking'' and ``running''. I have worked almost all of
these problems up to the end of chapter 10 and have typed up fairly
comprehensive solutions in LaTeX. Some of my students complained
that the problems were either trivially easy (the ``walking'' problems)
or excessively difficult (the ``running'' problems). There is some
truth in their complaint, some of the ``running'' problems were exceptionally
difficult for a student at this level. There are answers to a reasonable
number of the problems at the end of the book, but no hints on how to
solve a problem if a student gets stuck. Despite their complaints,
overall I think the authors have done a reasonable job with the exercises.
Some exercises clearly extend the material in the chapters and some
provide additional mathematical insight into the material. This is what
an instructor is looking for in exercises. Some chapters had a lot of
exericses, for example there are 49 for the chapter on compound interest.
If you are looking for textbook so students can get their foot on the
first rung of the ladder of financial mathematics then this is quite a
good one. Its theorem-proof approach is not suitable for the general finance
student, but for ones who are serious about learning the quantitative
side of finance this book can safely be used at the 2nd year undergraduate
level (US sophomore).
I think people award stars far too generously and I may be guilty of that practice
in this review. My final assessment of four stars is partly because there was little else
to choose from when I selected it as the text for the course (though that
is changing) and it does have some weaknesses. However, overall it
is a good place to start if you are looking for a text for the most
basic financial mathematics course.
8 of 11 people found the following review helpful.
painless introduction
By A. Ali
A nifty little book that painlessly introduces interest rates, annuities, amortisation, bonds, stock markets, and options (it even has an elementary proof of Black-Scholes). Recommended for MBA types and numerate laymen who want a peek at the arcane world of finance.
0 of 6 people found the following review helpful.
This book is terrible, just terrible
By J. Kennish
Or maybe my professor is terrible? I had a really difficult time understanding the flow of the book, and felt pretty dumb about it. It's heavy in math proofs, which is cool, but seems less concerned with financial problems. Or maybe my professor just didn't assign good chapters. Either way, my impression of this book is not good.
See all 3 customer reviews...
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