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Mathematical Interest Theory provides an introduction to how
investments grow over time. This is done in a mathematically precise
manner. The emphasis is on practical applications that give the reader
a concrete understanding of why the various relationships should be
true. Among the modern financial topics introduced are: arbitrage,
options, futures, and swaps. Mathematical Interest Theory is written
for anyone who has a strong high-school algebra background and is
interested in being an informed borrower or investor. The book is
suitable for a mid-level or upper-level undergraduate course or a
beginning graduate course.
The content of the book, along with an understanding of
probability, will provide a solid foundation for readers embarking on
actuarial careers. The text has been suggested by the Society of
Actuaries for people preparing for the Financial Mathematics exam. To
that end, Mathematical Interest Theory includes more than 260
carefully worked examples. There are over 475 problems, and numerical
answers are included in an appendix. A companion student solution
manual has detailed solutions to the odd-numbered problems. Most of
the examples involve computation, and detailed instruction is provided
on how to use the Texas Instruments BA II Plus and BA II Plus
Professional calculators to efficiently solve the problems. This
Third Edition updates the previous edition to cover the material in
the SOA study notes FM-24-17, FM-25-17, and FM-26-17.
Undergraduate and graduate students interested in preparing for the Society of Actuaries (SOA) Financial Mathematics (FM) exam.
This book is a systematic account of the
impressive developments in the theory of symmetric manifolds achieved
over the past 50 years. It contains detailed and friendly, but
rigorous, proofs of the key results in the theory. Milestones are the
study of the group of holomomorphic automorphisms of bounded domains
in a complex Banach space (Vigué and Upmeier in the late 1970s),
Kaup's theorem on the equivalence of the categories of symmetric
Banach manifolds and that of hermitian Jordan triple systems, and the
culminating point in the process: the Riemann mapping theorem for
complex Banach spaces (Kaup, 1982). This led to the introduction of
wide classes of Banach spaces known as \(\mathrm{JB}^*\)-triples
and \(\mathrm{JBW}^*\)-triples whose geometry has been
thoroughly studied by several outstanding mathematicians in the late
1980s.
The book presents a good example of fruitful interaction between
different branches of mathematics, making it attractive for
mathematicians interested in various fields such as algebra,
differential geometry and, of course, complex and functional analysis.
This book is published in cooperation with Real Sociedad Matemática Española (RSME)
Graduate students interested in complex analysis and the theory of Banach spaces.
A great many students have participated annually in the Annual High School Mathematics Examination (AHSME) sponsored by the Mathematical Association of America (MAA) and four other national organizations in the mathematical sciences. In 1960, 150,000 students participated from about 5,200 high schools. In 1980, 416,000 students participated from over 6,800 high schools. Since 1950, when the first of these examinations was given, American high school students have tested their skills and ingenuity on such problem as: The rails on a railroad are 30 feet long. As the train passes over the point where the rails are joined, there is an audible click. The speed of the train in miles per hour is approximately the number of clicks heard in how many seconds? And many others, based on the high school curriculum in mathematics.
Every year, 100 of the most mathematically
talented high school students in the country compete in the USA
Mathematical Olympiad (USAMO). The USAMO is the third stage of a
three-tiered mathematical competition for high school students in the
United States and Canada that begins with the AHSME taken by over
400,000 students, continues with the American Invitational Mathematics
Exam involving 2,000 students, and culminates with the 100-contestant
USAMO.
Winners of the USAMO go on to compete in the International
Mathematical Olympiad. Compilation of 116 problems of arresting
ingenuity given to high school students competing in the International
Mathematical Olympiads. All are accessible to secondary school
students. The alternative solutions are particularly interesting
because they show that there are many ways to solve a problem.
Many mathematicians have been drawn to mathematics through their
experience with math circles: extracurricular programs
exposing teenage students to advanced mathematical topics and a myriad
of problem solving techniques and inspiring in them a lifelong love
for mathematics. Founded in 1998, the Berkeley Math Circle
(BMC) is a pioneering model of a U.S. math circle, aspiring
to prepare our best young minds for their future roles as mathematics
leaders. Over the last decade, 50 instructors—from university
professors to high school teachers to business tycoons—have
shared their passion for mathematics by delivering more than 320 BMC
sessions full of mathematical challenges and wonders.
Based on a dozen of these sessions, this book encompasses a wide
variety of enticing mathematical topics: from inversion in the plane
to circle geometry; from combinatorics to Rubik's cube and abstract
algebra; from number theory to mass point theory; from complex numbers
to game theory via invariants and monovariants. The treatments of
these subjects encompass every significant method of proof and
emphasize ways of thinking and reasoning via 100 problem solving
techniques. Also featured are 300 problems, ranging from beginner to
intermediate level, with occasional peaks of advanced problems and
even some open questions.
The book presents possible paths to
studying mathematics and inevitably falling in love with it, via
teaching two important skills: thinking creatively while still
“obeying the rules,” and making connections between
problems, ideas, and theories. The book encourages you to apply the
newly acquired knowledge to problems and guides you along the way, but
rarely gives you ready answers. “Learning from our own
mistakes” often occurs through discussions of non-proofs and
common problem solving pitfalls. The reader has to commit to mastering
the new theories and techniques by “getting your hands
dirty” with the problems, going back and reviewing necessary
problem solving techniques and theory, and persistently moving forward
in the book. The mathematical world is huge: you'll never know
everything, but you'll learn where to find things, how to
connect and use them. The rewards will be substantial.
In the interest of fostering a greater awareness and appreciation of
mathematics and its connections to other disciplines and everyday life, MSRI
and the AMS are publishing books in the Mathematical Circles Library series as
a service to young people, their parents and teachers, and the mathematics
profession.
Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).
High school teachers and students interested in mathematical problem solving; college professors and research mathematicians interested in the mathematical education of talented middle and high school students.
. . . [F]rom the authors' Introduction and the Foreword by Robert L. Bryant, Director of the Mathematical Science Research Institute (MSRI), 'Math circles . . . all have one thing in common: to inspire in students an understanding of and lifelong love for mathematics.' The book, based on the notes from several sessions of the Berkeley Math Circle (BMC), reaches that goal beautifully. It is written with enthusiasm and flair; the book breathes love for mathematics and the desire to convey and share it with the reader. . . . The editors deserve praise for producing a coherent style that is followed throughout. . . . On the whole, the book is thoughtfully organized and well written. . . . [A] welcome beginning for the emerging tradition in the US math education.
-- Alex Bogomolny, MAA Reviews
This book is superbly written by a world-leading expert on
partial differential equations and differential geometry. It consists
of two parts. Part I covers the existence and uniqueness of solutions
of elliptic differential equations. It is direct, to the point,
moves smoothly and quickly, and there are no unnecessary
discussions or digressions. Many topics discussed in Part II will be
new and surprising to many students, even to some experts in
differential geometry.
Both the selection of topics and the exposition are excellent. The
detailed discussion of the case of surfaces motivated the later
analogues in the higher dimensions.
A publication of Higher Education Press (Beijing). Exclusive rights in North America; non-exclusive outside of North America. No distribution to mainland China unless order is received through the AMS bookstore. Online bookstore rights worldwide. All standard discounts apply.
Graduate students and research mathematicians interested in differential equations and geometry.
This volume contains the proceedings of the
2016 Summer School on Fractal Geometry and Complex Dimensions, in
celebration of Michel L. Lapidus's 60th birthday, held from June
21–29, 2016, at California Polytechnic State University, San
Luis Obispo, California.
The theme of the contributions is fractals and dynamics and content
is split into four parts, centered around the following themes:
Dimension gaps and the mass transfer principle, fractal strings and
complex dimensions, Laplacians on fractal domains and SDEs with
fractal noise, and aperiodic order (Delone sets and tilings).
Graduate students and research mathematicians interested in fractal geometry, dynamical systems, and related areas.
The quadratic formula for the solution of quadratic equations was discovered independently by scholars in many ancient cultures and is familiar to everyone. Less well known are formulas for solutions of cubic and quartic equations whose discovery was the high point of 16th century mathematics. Their study forms the heart of this book, as part of the broader theme that a polynomial's coefficients can be used to obtain detailed information on its roots. The book is designed for self-study, with many results presented as exercises and some supplemented by outlines for solution. The intended audience includes in-service and prospective secondary mathematics teachers, high school students eager to go beyond the standard curriculum, undergraduates who desire an in-depth look at a topic they may have unwittingly skipped over, and the mathematically curious who wish to do some work to unlock the mysteries of this beautiful subject.
This book, written to enable self-study, addresses the problem of determining zeros of polynomials from their coefficients, avoiding modern abstract algebra and Galois theory. Irving (Univ. of Washington) developed this work from a course he taught to prospective and in-service secondary school teachers, and it would make welcome reading for any undergraduate interested in seeing some classical algebra that is no longer a regular part of the school curriculum. The author begins with a careful derivation of the quadratic formula to produce Cardano's formula for roots of cubic equations and Euler's formula for solving quartic equations as natural counterparts. Along the way, he constructs the various discriminants for determining the number of distinct real roots, as well as complex arithmetic from scratch. The volume culminates with a discussion of higher-order polynomial equations and a proof of the fundamental theorem of algebra. Irving weaves together the mathematics and the historical development of the methods throughout the book. Exercises form an integral part of the text and are embedded in the exposition so that the reader can be a partner in constructing the algebraic arguments.
-- S.J. Colley, CHOICE Magazine
While the content does go beyond the quadratic formula, that distance is not great. The first four-fifths of the book is a historical and developmental walk through the tactics used to solve polynomials from quadratics up through degree four polynomials. The final section deals with quintic polynomials and the fundamental theorem of algebra. The level of material is generally well within the skill set of the advanced high school student, there are many formulas, although there is also real value in the historical details. For the student thinking about math as a career it is a demonstration of how mathematics has evolved over time at an uncertain pace. Equations considered impossible to solve are "suddenly" rendered solvable by one or more mathematicians that develop the correct approach or a dramatically different way of representing things. The best example of this is the development of the complex numbers. Originally used with reluctance, they changed an entire set of equations from those considered impossible to solve to ones that can be easily solved by modern high school students. Several exercises are embedded in the text, no solutions are included. For most people this will not be a problem as they will be able to develop the solutions on their own. This is a solid resource for high school mathematics, the material is well presented. i would be comfortable with giving it to a good student and telling them to learn it on their own and contact me if you need help.
-- Charles Ashbacher, Journal of Recreational Mathematics
… There is a great deal to like about this book. It is clearly written and will teach the reader a lot of mathematics that current undergraduates may rarely see. Future teachers, in particular, may find quite a lot of value here, since it clearly conveys the idea that the standard quadratic formula, which most students find boring, is really the tip of a very interesting iceberg.
-- Mark Hunacek, MAA Review
Fourier Series, Fourier Transforms, and Function Spaces is
designed as a textbook for a second course or capstone course in
analysis for advanced undergraduate or beginning graduate students.
By assuming the existence and properties of the Lebesgue integral,
this book makes it possible for students who have previously taken
only one course in real analysis to learn Fourier analysis in terms of
Hilbert spaces, allowing for both a deeper and more elegant approach.
This approach also allows junior and senior undergraduates to study
topics like PDEs, quantum mechanics, and signal processing in a
rigorous manner.
Students interested in statistics (time series), machine learning
(kernel methods), mathematical physics (quantum mechanics), or
electrical engineering (signal processing) will find this book useful.
With 400 problems, many of which guide readers in developing key
theoretical concepts themselves, this text can also be adapted to
self-study or an inquiry-based approach. Finally, of course, this
text can also serve as motivation and preparation for students going
on to further study in analysis.
Undergraduate and graduate students and researchers interested in analysis, differential equations, and applied math.
Reprinted edition available: TEXT/55
Combinatorics is mathematics of enumeration,
existence, construction, and optimization questions concerning finite
sets. This text focuses on the first three types of questions and
covers basic counting and existence principles, distributions,
generating functions, recurrence relations, Pólya theory,
combinatorial designs, error correcting codes, partially ordered sets,
and selected applications to graph theory including the enumeration of
trees, the chromatic polynomial, and introductory Ramsey theory. The
only prerequisites are single-variable calculus and familiarity with
sets and basic proof techniques.
The text emphasizes the brands of
thinking that are characteristic of combinatorics: bijective and
combinatorial proofs, recursive analysis, and counting problem
classification. It is flexible enough to be used for undergraduate
courses in combinatorics, second courses in discrete mathematics,
introductory graduate courses in applied mathematics programs, as well
as for independent study or reading courses. What makes this text a
guided tour are the approximately 350 reading questions spread
throughout its eight chapters. These questions provide checkpoints for
learning and prepare the reader for the end-of-section exercises of
which there are over 470. Most sections conclude with Travel Notes
that add color to the material of the section via anecdotes, open
problems, suggestions for further reading, and biographical
information about mathematicians involved in the
discoveries.
This is a well-written, reader-friendly, and self-contained undergraduate course on combinatorics, focusing on enumeration. The book includes plenty of exercises, and about half of them come with hints.
-- M. Bona, Choice Magazine
… The delineation of the topics is first rate—better than I have ever seen in any other book. … CAGT has both good breadth and great presentation; it is in fact a new standard in presentation for combinatorics, essential as a resource for any instructor, including those teaching out of a different text. For the student: If you are just starting to build a library in combinatorics, this should be your first book.
-- The UMAP Journal
… [This book] is an excellent candidate for a special topics course for mathematics majors; with the broad spectrum of applications that course can simultaneously be an advanced and a capstone course. This book would be an excellent selection for the textbook of such a course. … This book is the best candidate for a textbook in combinatorics that I have encountered.
-- Charles Ashbacher