Logicomix: An Epic Search for Truth is a graphic novel about the foundational quest in mathematics, written by Apostolos Doxiadis, author of Uncle Petros and Goldbach's Conjecture, and theoretical computer scientist Christos Papadimitriou of the University of California, Berkeley. Character design and artwork are by Alecos Papadatos and color is by Annie Di Donna.
This is a beginner's guide with clear step-by-step instructions,
explanations, and advice. Each concept is illustrated with a complete
example that you can use as a starting point for your own work. If you
are an engineer, scientist, mathematician, or student, this book is for
you. To get the most from Sage by using the Python programming language,
we'll give you the basics of the language to get you started. For this,
it will be helpful if you have some experience with basic programming
concepts.
This work stresses the illogical manner in which mathematics has developed, the question of applied mathematics as against 'pure' mathematics, and the challenges to the consistency of mathematics' logical structure that have occurred in the twentieth century.
A First Course in Probability, Eighth Edition, features clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus.
Going beyond the conventional mathematics of probability theory, this
study views the subject in a wider context. It discusses new results,
along with applications of probability theory to a variety of problems.
The book contains many exercises and is suitable for use as a textbook
on graduate-level courses involving data analysis. Aimed at readers
already familiar with applied mathematics at an advanced undergraduate
level or higher, it is of interest to scientists concerned with
inference from incomplete information.
This new-in-paperback edition provides a general introduction to
algebraic and arithmetic geometry, starting with the theory of schemes,
followed by applications to arithmetic surfaces and to the theory of
reduction of algebraic curves. The first part introduces basic objects
such as schemes, morphisms, base change, local properties (normality,
regularity, Zariski's Main Theorem) This is followed by the more global
aspect: coherent sheaves and a finiteness theorem for their cohomology
groups. Then follows a chapter on sheaves of differentials, dualizing
sheaves, and Grothendieck's duality theory. The first part ends with the
theorem of Riemann-Roch and its application to the study of smooth
projective curves over a field. Singular curves are treated through a
detailed study of the Picard group. The second part starts with
blowing-ups and desingularization (embedded or not) of fibered surfaces
over a Dedekind ring that leads on to intersection theory on arithmetic
surfaces. Castelnuovo's criterion is proved and also the existence of
the minimal regular model. This leads to the study of reduction of
algebraic curves. The case of elliptic curves is studied in detail. The
book concludes with the fundamental theorem of stable reduction of
Deligne-Mumford. This book is essentially self-contained, including the
necessary material on commutative algebra. The prerequisites are few,
and including many examples and approximately 600 exercises, the book is
ideal for graduate students.
This is a description of the underlying principles of algebraic
geometry, some of its important developments in the twentieth century,
and some of the problems that occupy its practitioners today. It is
intended for the working or the aspiring mathematician who is unfamiliar
with algebraic geometry but wishes to gain an appreciation of its
foundations and its goals with a minimum of prerequisites. Few algebraic
prerequisites are presumed beyond a basic course in linear algebra.