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Neuenschwander Dwight E.: Tensor
Calculus for Physics

Tensor Calculus for Physics

A Concise Guide

Handbook of Electronic Structure Theory provides a much-needed learning resource that collects and demonstrates the various key methods involved in electronic structure theory, the feasibility and reliability of electronic structure calculations and their applications using computational chemistry, with a particular focus on the most modern and recent problems which are poorly covered in existing, largely outdated book literature. This handbook is designed with early career researcher learning in mind by aiming to provide a careful, structured, coherent, measured, and incremental presentation of the subject matter as well as appropriate problems and worked tutorial examples. Elements like summary boxes, worked examples, and downloadable data sets make this a holistic guide to the topic for learners from different backgrounds who require a deeper understanding of electronic structure theory. Part I one of the book focuses on the critical core theories, before Part II moves on to some of the most important recent developments and their potential future directions, including key topics such as the electronic excited states and the harnessing of machine learning. Finally, Part III then collects a range of key case study examples of applications such as for biomolecules, in spectroscopy, or for use in catalysis amongst others. Handbook of Electronic Structure Theory is written primarily for masters, PhD, and postdoctoral students in theoretical and computational chemistry as well as experimental researchers wishing to apply quantum chemical methods in a critical way. The book will also have significant relevance to those studying and teaching in the adjacent fields of computational physics, materials science, and astrochemistry, who are making use of electronic structure methods. It is also likely to be of interest to chemists working on designing new materials and compounds targeting industrial and environmental applications such as catalysis, energy harvesting or green chemistry.

Methods and Applications

Handbook of Electronic Structure Theory

The aim of this textbook is to improve students' ability to formulate economic problems and provide essential mathematical tools for analysis across various contexts. This book presents the author's current understanding of mathematics, shaped by several years of teaching this subject as well as enriched through interactions with his students. To aid students in their learning, the book is written in a manner that better highlights key concepts and provides additional clarity when possible. In this way, it is hoped that students will feel more guided in their study of mathematics and its applications in microeconomics.

Essential Mathematics For Microeconomics: A Student's Guide To Key Mathematical Techniques

Why Not Nonlinear Algebra: Math, Science, Applications And Funding

Many of the deepest and most important areas of mathematics have arisen from questions about extremes - shortest lines, smallest areas, densest packings, fewest colours. Mathematicians have been grappling with such issues for centuries, and some go back thousands of years. The isoperimetric problem, for example - which asks for the shortest path enclosing a given area - dates back to the mythological founding of the city of Carthage. By contrast, it was only in 2017 that the densest ways to pack identical spheres into a space of 24 dimensions was finally proved. Many of these problems are more than mere thought experiments. The origins of the Travelling Salesperson Problem - find the shortest route that visits a given set of cities - are self-explanatory. The Plateau problem, about the geometry of soap bubbles, now has applications as diverse as cosmology and biological development. Reaching for the Extreme tells the stories of these and other similar problems: their historical roots, the struggles to solve them, and the uses that can be made of the results, when such uses exist.

How the Quest for the Biggest, Fewest and Weirdest Makes Maths

Reaching for the Extreme

While the field of Deep Learning has been advancing at frightening speeds during the last ten years, we do not have a plausible theoretical explanation of its success yet. One can safely say that Deep Learning works, but nobody really understands why. Nevertheless, starting around five years before now, a decent number of theoretical papers specifically concerning neural nets started to emerge at top machine learning venues. This makes us think that the core of Deep Learning theory has already started to crystallize.The goal of the present book is to present these core concepts of Deep Learning theory to readers so that they could directly dive into recent papers of this area. For this purpose, each chapter elaborates a simple model or a classical result in details first and then discusses possible generalizations and more recent developments of the same idea.We have to warn the reader that the present book is not a mathematical manuscript. Not all results here are stated as formal theorems and not all theorems are provided with complete and rigorous proofs. Many of the theorems of the book are proven up to some technical lemmas, while for some there is only a proof sketch. This conforms with the main idea of the book: present and illustrate concepts rather than reproduce all the results.The book, in its present form, covers the following topics: uniform generalization bounds, PAC-bayesian generalization bounds, double descent phenomena, infinitely-wide networks, implicit bias of gradient descent, loss landscape, gradient descent convergence guarantees, and initialization strategies.

Elements Of Deep Learning Theory

Corwin Mathematics Series

Practical and proven math tasks to maximize student thinking and learning
Building upon the blockbuster success of Building Thinking Classrooms in Mathematics, Peter Liljedahl has joined forces with co-author Kyle Webb to bring the Building Thinking Classrooms (BTC) framework to life in this new book, Mathematics Tasks for the Thinking Classroom, Grades 6-12.
But this book is so much more than simply a collection of good thinking tasks. It delves deeper into the implementation of the 14 practices from the BTC framework by updating the practices with the newest research, and focusing on the practice through the lens of rich math tasks that address specific mathematical learning outcomes or standards. Across the 20 non-curricular tasks and 30 curricular tasks used as models, this book:
<ul>
 <li>Helps you choose tasks to fit your particular math standards, goals, and the competencies you want your students to build</li>
 <li>Walks you through all the steps and scripts to launch, facilitate, and consolidate each task</li>
 <li>Shares examples of possible student solutions along with hints you might offer to help their thinking along</li>
 <li>Offers tasks for consolidation, example notes to my future forgetful self, and mild, medium, and spicy check-your-understanding questions (CYUs) for every thin sliced sequences of curricular tasks</li>
 <li>Imparts reflections from the authors on each task</li>
</ul>
The book closes with specific guidance on how to find more tasks or craft your own non-curricular and curricular tasks, along with answers to educators' frequently asked questions. It includes access to a companion website that includes downloadables and a task template for creating your own tasks.
Whether you are new to BTC or a seasoned user, Mathematics Tasks for the Thinking Classroom, Grades 6-12 will help teachers, coaches, and specialists transform traditional math classrooms into dynamic and thought-provoking learning spaces. Mathematics Tasks for the Thinking Classroom, Grades K-5 is also available to create district-wide thinking classrooms!

Mathematics Tasks for the Thinking Classroom, Grades 6-12

Medical Dosage Calculations For Dummies

Smart Thinking

A new smart-thinking series that applies complex mathematical ideas to everyday scenarios.

Mathematical answers to life’s key questions

Why Don’t Rabbits Rule The World?

This book covers complex analysis (the study of boundary behaviors of analytic functions) and its applications with engineering problems, especially control theory from the viewpoint of boundary functions. The metascience part is rather unique and illustrates a metascientific way of thinking engineering problems by examples of batteries which are cores of electric vehicles.This book gives a way of looking at the phenomena from a higher and brighter point of view through the windows of boundary behavior and metascience. In Chapter 1 which is meant for mathematics-oriented readers, we state materials in standard complex analysis with emphasis on similarity and Laurent expansions. Non-mathematical readers can also benefit by browsing through many examples and worked-out exercises. Chapter 2 gives some concrete examples of invoking novel ideas in the heap of stereo-typed contributions to a field. Possible replacement of LIB by ECaSS(R) is a typical example through which the reader can learn basics of electromagnetism and electrochemistry. The book also provides hints for a deeper understanding of environmental problems as well as how to manage and create a sustainable society.

From Complex Analysis To Metascience: A Stroll Around Boundary Behavior, Similarity And Duality

An accessible resource to help you puzzle out logic concepts Logic For Dummies, 2nd Edition explains all the varied ways we use logic in philosophy, science, and everyday life. College students taking a logic course and lifelong learners alike can benefit from this accessible guide to logic concepts--such as syllogisms, constructing proofs and refutations, propositional and predicate logic, symbolic logic, modal and fuzzy logic, deductive and inductive reasoning, and beyond. With real-world examples, fun logic problems, and fully worked out proofs, you have plenty of opportunities to follow along and apply what you've learned. Logic For Dummies, 2nd Edition helps you connect the logical dots! Inside: <ul> <li>Grasp formal and informal logic with clear explanations and practice problems</li> <li>See how logic shows up in everyday life and discover how to spot logical fallacies</li> <li>Work through logical proofs and refutations, with answer explanations to strengthen your understanding</li> <li>Sharpen your ability to reason through complex issues with truth tables</li> </ul> Logic For Dummies, 2nd Edition is the logical choice for anyone who wants or needs to learn the concepts, theories, and formulas of logical reasoning.

Logic For Dummies

A Guide to Navigating Defaults and Managing Sovereign Fixed Income Portfolios

The Sovereign Debt Investor

Tensor Calculus for Physics

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