Series: Classroom Resource Material
Hardback (ISBN-13: 9780883857472)
In the second edition of this MAA classic, exploration continues
to be an essential component. More than 60 new exercises have
been added, and the chapters on infinite summations,
differentiability and continuity, and convergence of infinite
series have been reorganized to make it easier to identify the
key ideas. A Radical Approach to Real Analysis is an introduction
to real analysis, rooted in and informed by the historical issues
that shaped its development. It can be used as a textbook, or as
a resource for the instructor who prefers to teach a traditional
course, or as a resource for the student who has been through a
traditional course yet still does not understand what real
analysis is about and why it was created.
* The historically motivated approach provides context and
insight
* Shows that experimentation is an essential component in the
growth of mathematics
* Extra web resources including Maple and Mathematica commands,
hints and selected solutions to exercises, and additional
exercises and projects, can be found at www.macalester.edu/aratra
Contents
Preface; 1. Crisis in mathematics: Fourier's series; 2. Infinite
summations; 3. Differentiability and continuity; 4. The
convergence of infinite series; 5. Understanding infinite series;
6. Return to Fourier series; 7. Epilogue; A. Explorations of the
infinite; B. Bibliography; C. Hints to selected exercises.
Reviews
1st edition: 'The past decade or so has witnessed the appearance
of a substantial number of 'bridge the gap' introductions to real
analysis, which lead the students at a gentler pace through the
fundamentals of real analysis according to the traditional
syllabus. It is well worth considering whether students in their
undergraduate real analysis course might be better served by a
radical approach such as Bressoud's.' G. A. Heuer, Mathematical
Reviews
1st edition: 'It will appeal as a text; it should be in every
library as a reference.' Wayne Roberts, Choice
Series: Spectrum
Hardback (ISBN-13: 9780883855577)
The Professor in Owen O'Shea's book is the imaginary American
Richard Stein. As Owen O'Shea and the Professor travel through
Ireland, O'Shea notes the Professor's collection of amazing magic
numbers in fascinating detail. His mathematical curiosities are
wide ranging, concerning the 1915 sinking of the Lusitania to
coincidences about Apollo 11 to the first moon walk to new
numerical curiosities. The new curiosities, among many others,
center on Presidents Lincoln and Kennedy; the USA and Ireland;
the two World Wars; the King James Version of the Bible, and
James Joyce. The Number of the Beast, 666, is discussed as well,
as are many new equations involving that famous number - all
appearing here for the first time. And for those fascinated by
games and gambling, a number of curious proposition bets
involving dice, darts, and playing cards, and various
mathematical puzzles are scattered throughout this singularly
entertaining book.
* A fascinating collection of numerical curiosities and wonders
* Foreword by Martin Gardner
* Many mathematical puzzles are posed and answers are provided to
each of these stimulating conundrums
Contents
Foreword by Martin Gardner; Introduction; 1. Digit curiosities; 2.
The 9/11 atrocities; 3. The Professor speaks on the U. S. and
Ireland; 4. Curiosities in armed conflicts; 5. Number and word
palindromes; 6. The U. S.-Iraq war; 7. The number of the Beast; 8.
Curios of the Lusitania and other curious matters; 9. Wordplay
and other curiosities; 10. New coincidences on Lincoln and
Kennedy; 11. Dart and card curiosities; 12. The Professor gives
some number patterns; 13. The King James Bible and some currency
curiosities; 14. The Professor at the university; Index; About
the authors.
Reviews
'Owen O'Shea, more than anyone, has the uncanny ability to find
remarkable coincidences everywhere he looks. How he does it is a
mystery. Some (not all!) of his astounding discoveries are packed
into this entertaining mind bewildering book.' Martin Gardner
From the Number of the Beast and triangular numbers to Friedman
numbers and pandigital squares, this smorgasbord of mathematical
puzzles, curiosities and coincidences is sure to delight readers
of all level of mathematical sophistication.' Clifford A.
Pickover, author of The Mobius Strip and A Passion for
Mathematics
Series: Mathematical Sciences Research Institute Publications
Hardback (ISBN-13: 9780521874922)
Paperback (ISBN-13: 9780521697668)
Testing matters! It can determine kids' and schools' futures. In
a conference at the Mathematical Sciences Research Institute,
mathematicians, maths education researchers, teachers, test
developers, and policymakers gathered to work through critical
issues related to mathematics assessment. They examined:
* The challenges of assessing student learning in ways that
support instructional improvement;
* Ethical issues related to assessment, including the impact of
testing on urban and high-poverty schools;
* The different (and sometimes conflicting) needs of the
different groups; and
* Different frameworks, tools, and methods for assessment,
comparing the kinds of information they offer about students'
mathematical proficiency.
This volume presents the results of the discussions. It
highlights the kinds of information that different assessments
can offer, including many examples of some of the best
mathematics assessments worldwide. A special feature is an
interview with a student about his knowledge of fractions and a
demonstration of what interviews (versus standardized tests) can
reveal.
* Offers examples of very different ways to understand what
students know in mathematics
* A 'live' interview with a student and what it reveals about
understanding
* Reveals what testing does and does not tell you and can tell
you
Contents
Preface Alan H. Schoenfeld; Part I. The Big Picture: 1. Issues
and tensions in the assessment of mathematical proficiency Alan H.
Schoenfeld; 2. Crucial contemporary social, political, and
cultural issues in mathematical assessment in the United States
Judith Ramaley; 3. Crucial contemporary social, political, and
cultural issues in mathematical assessment in the United States
Susan Sclafani; Part II. Perspectives on Mathematical Proficiency:
4. What is mathematical proficiency? R. James Milgram; 5. What is
mathematical proficiency (and how can it be assessed)? Alan H.
Schoenfeld; Part III. What Does Assessment Assess? Issues and
Examples: 6. Assessing mathematical proficiency: what is
important? Hugh Burkhardt; 7. Aspects of the art of assessment
design Jan de Lange; 8. Mathematical proficiency for citizenship
Bernard Madison; 9. Learning from assessment Richard Askey; 10.
Using assessment to design professional development David Foster;
Part IV. The Case of Algebra: 11. Context and learning: an
assessment of 'real world' mathematics tasks Ann Shannon; 12.
Making meaning in algebra: examining students’ understandings
and misconceptions David Foster; 13. Assessing the strands of
student proficiency in elementary algebra William McCallum; Part
V. What Do Different Assessments Assess?: 14. Learning about
fractions from assessment Linda Fisher; 15. Brandon interview and
commentary, plus CD of interview Deborah Ball; Part VI. The
Importance of Context: 16. Assessment of mathematics learning in
France Michele Artigue; 17. Assessment to improve learning in
mathematics: the BEAR assessment system Mark Wilson and Claus
Carstensen; 18. English learners and math learning: language
issues for the math educators to consider Lily W. Fillmore; 19.
Beyond words to mathematical content: assessing English language
learners in the mathematics classroom Judit Moschkovich; 20.
Assessment in the real world: the case of New York city Elizabeth
Taleporos; 21. Perspectives on state assessments in California
Elizabeth Stage; Part VII. What Do We Need To Know?: 22. Research
agenda emerging from the conference.
Paperback (ISBN-13: 9780521699273)
The detailed, practical, step-by-step advice in this user-friendly
guide will help students and researchers to communicate their
work more effectively through the written word. Covering all
aspects of the writing process, this concise, accessible resource
is critically acclaimed, well-structured, comprehensive, and
entertaining. Self-help exercises and abundant examples from
actual typescripts draw on the authors' extensive experience
working both as researchers and with them. Whilst retaining the
user-friendly and pragmatic style of earlier editions, this third
edition has been updated and broadened to incorporate such timely
topics as guidelines for successful international publication,
ethical and legal issues including plagiarism and falsified data,
electronic publication, and text-based talks and poster
presentations. With advice applicable to many writing contexts in
the majority of scientific disciplines, this book is a powerful
tool for improving individual skills and an eminently suitable
text for classroom courses or seminars.
* Offers extremely pragmatic and comprehensive step-by-step
coverage of all aspects of scientific presentation, in a well-structured,
entertaining style
* The advice is practical, having arisen from the authors' own
cumulative experience as working scientists, editors, and mentors
* Self-help exercises based on actual scientific manuscripts
reinforce concepts and allow writers to practice the techniques
that are presented
Contents
1. Preparing to write; 2. Composing a first draft; 3. Visual
support for the written word; 4. Visual support for the spoken
word; 5. Revising to increase coherence; 6. The second revision:
word choice and style; 7. Attending to grammar, numbers and other
mechanics; 8. The rest of the story.
Reviews
'This book is beyond reproach and should be regarded as
compulsory reading for all biomedical and science undergraduate
and postgraduate students and all others likely to have to write
or edit scientific reports.' Times Higher Education Supplement
'… very well organized and easy to scan for useful tips …
will soon become one of the more well-thumbed volumes on our
laboratory bookshelf.' Trends in Neuroscience
'… pragmatic, well-written and comprehensive … each stage -
from marshalling ideas through bashing out a first draft,
revising it, honing it for publication and correcting it in proof
- is demystified with exercises and examples.' New Scientist
Series: Cambridge Tracts in Mathematics (No. 172)
Hardback (ISBN-13: 9780521875240)
Dating back to work of Berthelot, rigid cohomology appeared as a
common generalization of Monsky-Washnitzer cohomology and
crystalline cohomology. It is a p-adic Weil cohomology suitable
for computing Zeta and L-functions for algebraic varieties on
finite fields. Moreover, it is effective, in the sense that it
gives algorithms to compute the number of rational points of such
varieties. This is the first book to give a complete treatment of
the theory, from full discussion of all the basics to
descriptions of the very latest developments. Results and proofs
are included that are not available elsewhere, local computations
are explained, and many worked examples are given. This
accessible tract will be of interest to researchers working in
arithmetic geometry, p-adic cohomology theory, and related
cryptographic areas.
* First book to give a complete treatment of the theory of rigid
cohomology, from full proofs for all the basics, to discussion of
the most recent developments
* Essential for specialists: contains proofs and results not
available elsewhere
* Accessible for non-specialists: written from a practical point
of view, with many worked examples
Contents
Introduction; 1. Prologue; 2. Tubes; 3. Strict neighborhoods; 4.
Calculus; 5. Overconvergent sheaves; 6. Overconvergent calculus;
7. Overconvergent isocrystals; 8. Rigid cohomology; 9. Epilogue;
Index; Bibliography.
Hardback (ISBN-13: 9780521847674)
Paperback (ISBN-13: 9780521612340)
orem proving. Because of this, students can find it very
difficult to make a successful transition from lectures to
examinations to practice, since the problems involved can vary so
much in nature. Since the subject is critical in many modern
applications such as mathematical finance, quantitative
management, telecommunications, signal processing,
bioinformatics, as well as traditional ones such as insurance,
social science andengineering, the authors have rectified
deficiencies in traditional lecture-based methods by collecting
together a wealth of exercises with complete solutions, adapted
to needs and skills of students. Following on from the success of
Probability and Statistics by Example: Basic Probability and
Statistics, the authors here concentrate on random processes,
particularly Markov processes, emphasising modelsrather than
general constructions. Basic mathematical facts are supplied as
and when they are needed andhistorical information is sprinkled
throughout.
* Enables readers to develop effective techniques for learning
about and developing a deeper understanding of probability and
statistics
* Contains a substantial number of Cambridge exam questions, and
solutions to help students prepare for examinations
* Will also aid students from other disciplines such as
engineering and social sciences - and those who need a background
in random processes for careers in finance, insurance, actuarial
studies and economics
Contents
Preface; Introduction: Andrei Markov and his time; 1. Discrete-time
Markov chains; 2. Continuous-time Markov chains: basic theory; 3.
Statistics of discrete-time Markov chains; Afterword: Pearson,
Maxwell and other famous Cambridge Wranglers of the past: some
lessons to be learned; Bibliography; Appendix; Index.
Series: Encyclopedia of Mathematics and its Applications (No.
113)
Hardback (ISBN-13: 9780521879897)
Recent years have seen an explosion of interest in stochastic
partial differential equations where the driving noise is
discontinuous. In this comprehensive monograph, two leading
experts detail the evolution equation approach to their solution.
Most of the results appear here for the first time in book form,
and the volume is sure to stimulate further research in this
important field. The authors start with a detailed analysis of
Levy processes in infinite dimensions and their reproducing
kernel Hilbert spaces; cylindrical Levy processes are constructed
in terms of Poisson random measures; stochastic integrals are
introduced. Stochastic parabolic and hyperbolic equations on
domains of arbitrary dimensions are studied, and applications to
statistical and fluid mechanics and to finance are also
investigated. Ideal for researchers and graduate students in
stochastic processes and partial differential equations, this
self-contained text will also interest those working on
stochastic modeling in finance, statistical physics and
environmental science.
* The first book to detail the evolution equation approach to the
solution of stochastic partial differential equations with Levy
noise
* Rapidly growing topic - majority of results appear here for the
first time
* Great potential for applications to finance, statistical
mechanics and fluid dynamics
Contents
Introduction; Part I. Foundations: 1. Why equations with Levy
noise?; 2. Analytic preliminaries; 3. Probabilistic
preliminaries; 4. Levy processes; 5. Levy semigroups; 6. Poisson
random measures; 7. Cylindrical processes and reproducing
kernels; 8. Stochastic integration; Part II. Existence and
Regularity: 9. General existence and uniqueness results; 10.
Equations with non-Lipschitz coefficients; 11. Factorization and
regularity; 12. Stochastic parabolic problems; 13. Wave and delay
equations; 14. Equations driven by a spatially homogeneous noise;
15. Equations with noise on the boundary; Part III. Applications:
16. Invariant measures; 17. Lattice systems; 18. Stochastic
Burgers equation; 19. Environmental pollution model; 20. Bond
market models; Appendix 1. Operators on Hilbert spaces; Appendix
2. C0-semigroups; Appendix 3. Regularization of Markov processes;
Appendix 4. Ito formulae; Appendix 5. Levy-Khinchin on [0,+ );
Appendix 6. Proof of Lemma; List of symbols; Bibliography; Index.