Advanced Lectures in Mathematics, Volume 33
Published: 17 April 2015
Languages: English, French
Paperback
440 pages
Contemporary mathematics in practice is both diversified and unified: There are many specializations, and most practitioners are comfortable only with a few of them; yet major advances in mathematics often rise from the unification of theories and methods drawn from greatly diverse specializations.
Introduction to Modern Mathematics presents a collection of expository introductions to, and surveys of, several active and important topics in mathematics. Contributors include some of the top mathematicians in the world, including two Fields medalists (Jones and Lafforgue) and a Shaw Prize winner (Taubes).
This volume should prove valuable to both beginners and experts, as an illuminating overview of current mathematics.
[Note: One article is written in French, the remainder in English]
This volume is part of the Advanced Lectures in Mathematics book series.
2015 Apr
9781571463050
paperback
7h x 10h
To Be Published: 19 May 2015
Paperback
278 pages
Lively and engaging articles from the lecturers and the participants of the 21st Gokova Geometry-Topology Conference, held on the shores of Gokova Bay, Turkey, in May of 2014.
This volume is part of the Gokova Geometry-Topology Conferences book series.
2015 May
9781571463074
paperback
7h x 10h
978-0-19-873691-2
Hardback
August 2015 (estimated)
Covers both time series and panel data analysis
Covers introductory as well as advanced topics in one volume
Comprehensive graduate text that combines theory and practice with many examples and empirical applications
All chapters contain supplementary exercises
Includes detailed cross references
This book is concerned with recent developments in time series and panel data techniques for the analysis of macroeconomic and financial data. It provides a rigorous, nevertheless user-friendly, account of the time series techniques dealing with univariate and multivariate time series models, as well as panel data models.
It is distinct from other time series texts in the sense that it also covers panel data models and attempts at a more coherent integration of time series, multivariate analysis, and panel data models. It builds on the author's extensive research in the areas of time series and panel data analysis and covers a wide variety of topics in one volume. Different parts of the book can be used as teaching material for a variety of courses in econometrics. It can also be used as reference manual.
It begins with an overview of basic econometric and statistical techniques, and provides an account of stochastic processes, univariate and multivariate time series, tests for unit roots, cointegration, impulse response analysis, autoregressive conditional heteroskedasticity models, simultaneous equation models, vector autoregressions, causality, forecasting, multivariate volatility models, panel data models, aggregation and global vector autoregressive models (GVAR). The techniques are illustrated using Microfit 5 (Pesaran and Pesaran, 2009, OUP) with applications to real output, inflation, interest rates, exchange rates, and stock prices.
Readership: Advanced undergraduates, graduates, and PhD students. Researchers at international agencies such as IMF, World Bank, and central banks.
Part I: Introduction to Econometrics
1: Relationship Between Two Variables
2: Multiple Regression
3: Hypothesis Testing in Regression Models
4: Heteroskedasticity
5: Autocorrelated Disturbances
6: Introduction to Dynamic Economic Modelling
7: Predictability of Asset Returns and the EMH
Part II: Statistical Theory
8: Asymptotic Theory
9: Maximum Likelihood Estimation
10: Generalized Method of Moments
11: Model Selection and Testing Non-Nested Hypotheses
Part III: Stochastic Processes
12: Introduction to Stochastic Processes
13: Spectral Analysis
Part IV: Univariate Time Series Models
14: Estimation of Stationary Time Series Processes
15: Unit Root Processes
16: Trend and Cycle Decomposition
17: Introduction to Forecasting
18: Measurement and Modelling of Volatility
Part V: Multivariate Time Series Models
19: Multivariate Analysis
20: Multivariate Rational Expectations Models
21: Vector Autoregressive Models
22: Cointegration Analysis
23: VARX Modelling
24: Impulse Response Analysis
25: Modelling the Conditional Correlation of Asset Returns
Part VI: Panel Data Econometrics
26: Panel Data Models with Strictly Exogenous Regressors
27: Short T Dynamic Panel Data Models
28: Large Heterogeneous Panel Data Models
29: Cross Section Dependence in Panels
30: Spatial Panel Econometrics
31: Unit Roots and Cointegration in Panels
32: Aggregation of Large Panels
33: Theory and Practice of GVAR Modelling
Part VII: Appendices
A: Mathematics
B: Probability and Statistics
C: Bayesian Analysis
Series: Undergraduate Texts in Mathematics
2015
Includes insightful historical remarks regarding real analysis
Based on courses given at Eotvos Lorand University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable ? systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the studentfs mathematical intuition. The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated.
In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study.
Miklos Laczkovich is Professor of Mathematics at Eotvos Lorand University and the University College London, and was awarded the Ostrowski Prize in 1993 and the Szechenyi Prize in 1998. Vera T. Sos is a Research Fellow at the Alfred Renyi Institute of Mathematics, and was awarded the Szechenyi Prize in 1997.
Series: Undergraduate Texts in Mathematics
2015
Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonne, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis.
New to the second edition of Real Mathematical Analysis is a presentation of Lebesgue integration done almost entirely using the undergraph approach of Burkill. Payoffs include: concise picture proofs of the Monotone and Dominated Convergence Theorems, a one-line/one-picture proof of Fubini's theorem from Cavalierifs Principle, and, in many cases, the ability to see an integral result from measure theory. The presentation includes Vitalifs Covering Lemma, density points ? which are rarely treated in books at this level ? and the almost everywhere differentiability of monotone functions. Several new exercises now join a collection of over 500 exercises that pose interesting challenges and introduce special topics to the student keen on mastering this beautiful subject.
Charles C. Pugh is Professor Emeritus at the University of California, Berkeley. His research interests include geometry and topology, dynamical systems, and normal hyperbolicity.
Series: Applied Mathematical Sciences, Vol. 193
2015
The mathematical framework for a rigorous mathematical treatment of rate-independent systems, together with various applications, is presented in a comprehensive form for the first time
This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have been working on with a lot of collaborators over 15 years. The focus is mostly on fully rate-independent systems, first on an abstract level either with or even without a linear structure, discussing various concepts of solutions with full mathematical rigor. Then, usefulness of the abstract concepts is demonstrated on the level of various applications primarily in continuum mechanics of solids, including suitable approximation strategies with guaranteed numerical stability and convergence. Particular applications concern inelastic processes such as plasticity, damage, phase transformations, or adhesive-type contacts both at small strains and at finite strains. A few other physical systems, e.g. magnetic or ferroelectric materials, and couplings to rate-dependent thermodynamic models are considered as well. Selected applications are accompanied by numerical simulations illustrating both the models and the efficiency of computational algorithms.
In this book, the mathematical framework for a rigorous mathematical treatment of "rate-independent systems" is presented in a comprehensive form for the first time. Researchers and graduate students in applied mathematics, engineering, and computational physics will find this timely and well written book useful.
Alexander Mielke is Professor at Humboldt University of Berlin as well as a head of the research group "Partial Differential Equations" at the Weierstrass Institute for Applied Analysis and Stochastics. His research interest range over applied mathematical analysis, partial differential equations, multi-scale modeling and applications in continuum physics.
Toma Roubiek is a Professor at Charles University in Prague, as well as
a researcher at Institute of Thermomechanics and also at Institute of Information
Theory and Automation of the Czech Academy of Sciences. Having an engineering
background, his professional activity has evolved from computer simulations
of systems of nonlinear partial differential equations thru numerical mathematics
and optimization theory to applied mathematical analysis focused to mathematical
modeling in engineering and physics.