Meta Math!

Meta Math!
Author: Gregory Chaitin
Publisher: Vintage
Total Pages: 242
Release: 2006-11-14
Genre: Mathematics
ISBN: 1400077974

Gregory Chaitin, one of the world’s foremost mathematicians, leads us on a spellbinding journey, illuminating the process by which he arrived at his groundbreaking theory. Chaitin’s revolutionary discovery, the Omega number, is an exquisitely complex representation of unknowability in mathematics. His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.

Metamath: A Computer Language for Mathematical Proofs

Metamath: A Computer Language for Mathematical Proofs
Author: Norman Megill
Publisher: Lulu.com
Total Pages: 250
Release: 2019
Genre: Computers
ISBN: 0359702236

Metamath is a computer language and an associated computer program for archiving, verifying, and studying mathematical proofs. The Metamath language is simple and robust, with an almost total absence of hard-wired syntax, and we believe that it provides about the simplest possible framework that allows essentially all of mathematics to be expressed with absolute rigor. While simple, it is also powerful; the Metamath Proof Explorer (MPE) database has over 23,000 proven theorems and is one of the top systems in the "Formalizing 100 Theorems" challenge. This book explains the Metamath language and program, with specific emphasis on the fundamentals of the MPE database.

The AMTE Handbook of Mathematics Teacher Education

The AMTE Handbook of Mathematics Teacher Education
Author: Babette M. Benken
Publisher: IAP
Total Pages: 490
Release: 2024-02-01
Genre: Mathematics
ISBN:

This new volume of The Association of Mathematics Teacher Educators (AMTE) Professional Book Series is a critical and timely resource that paves the way and guides the future of mathematics teacher education. The collection of work in this AMTE Handbook of Mathematics Teacher Education reflects on research and what we know about how best to prepare and support both mathematics teachers and mathematics teacher educators and presents what is happening in the field. Examples included in the 22 chapters highlight how we are preparing teachers across multiple contexts (e.g., within district, in content courses for the major) and grade ranges (K-20+) and all chapters highlight relevant connections to the AMTE Standards for Preparing Teachers of Mathematics. Most importantly, this volume explores what we do not yet fully understand and where we are going. In essence, it considers how we can move the field forward. The 95 contributing authors range from graduate students to those who have served as leaders in the field in multiple ways for many years. Authors include K-12 teachers, school administrators, district leaders, graduate students, higher education faculty, and professional development facilitators.

Mathematics for Machine Learning

Mathematics for Machine Learning
Author: Marc Peter Deisenroth
Publisher: Cambridge University Press
Total Pages: 392
Release: 2020-04-23
Genre: Computers
ISBN: 1108569323

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Non-Newtonian Calculus

Non-Newtonian Calculus
Author: Michael Grossman
Publisher: Non-Newtonian Calculus
Total Pages: 108
Release: 1972
Genre: Mathematics
ISBN: 9780912938011

The non-Newtonian calculi provide a wide variety of mathematical tools for use in science, engineering, and mathematics. They appear to have considerable potential for use as alternatives to the classical calculus of Newton and Leibniz. It may well be that these calculi can be used to define new concepts, to yield new or simpler laws, or to formulate or solve problems.

Matheuristics

Matheuristics
Author: Vittorio Maniezzo
Publisher: Springer Science & Business Media
Total Pages: 283
Release: 2009-09-18
Genre: Business & Economics
ISBN: 1441913068

Metaheuristics support managers in decision-making with robust tools that provide high-quality solutions to important applications in business, engineering, economics, and science in reasonable time frames, but finding exact solutions in these applications still poses a real challenge. However, because of advances in the fields of mathematical optimization and metaheuristics, major efforts have been made on their interface regarding efficient hybridization. This edited book will provide a survey of the state of the art in this field by providing some invited reviews by well-known specialists as well as refereed papers from the second Matheuristics workshop to be held in Bertinoro, Italy, June 2008. Papers will explore mathematical programming techniques in metaheuristics frameworks, and especially focus on the latest developments in Mixed Integer Programming in solving real-world problems.

The Search for Certainty

The Search for Certainty
Author: Frank J. Swetz
Publisher: Courier Corporation
Total Pages: 194
Release: 2012-01-01
Genre: Mathematics
ISBN: 0486474429

Self-contained and authoritative, this history of mathematics is suited to those with no math background. Its absorbing, entertaining essays focus on the era from 1800 to 2000. Contributors include Henri Poincaré, Judith V. Grabiner, and H. S. M. Coxeter, who discuss topics ranging from logic and infinity to Fermat's Last Theorem.

A First Course in Mathematical Logic and Set Theory

A First Course in Mathematical Logic and Set Theory
Author: Michael L. O'Leary
Publisher: John Wiley & Sons
Total Pages: 464
Release: 2015-09-14
Genre: Mathematics
ISBN: 1118548019

A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.

Information-Driven Machine Learning

Information-Driven Machine Learning
Author: Gerald Friedland
Publisher: Springer Nature
Total Pages: 281
Release: 2024-01-02
Genre: Computers
ISBN: 3031394771

This groundbreaking book transcends traditional machine learning approaches by introducing information measurement methodologies that revolutionize the field. Stemming from a UC Berkeley seminar on experimental design for machine learning tasks, these techniques aim to overcome the 'black box' approach of machine learning by reducing conjectures such as magic numbers (hyper-parameters) or model-type bias. Information-based machine learning enables data quality measurements, a priori task complexity estimations, and reproducible design of data science experiments. The benefits include significant size reduction, increased explainability, and enhanced resilience of models, all contributing to advancing the discipline's robustness and credibility. While bridging the gap between machine learning and disciplines such as physics, information theory, and computer engineering, this textbook maintains an accessible and comprehensive style, making complex topics digestible for a broad readership. Information-Driven Machine Learning explores the synergistic harmony among these disciplines to enhance our understanding of data science modeling. Instead of solely focusing on the "how," this text provides answers to the "why" questions that permeate the field, shedding light on the underlying principles of machine learning processes and their practical implications. By advocating for systematic methodologies grounded in fundamental principles, this book challenges industry practices that have often evolved from ideologic or profit-driven motivations. It addresses a range of topics, including deep learning, data drift, and MLOps, using fundamental principles such as entropy, capacity, and high dimensionality. Ideal for both academia and industry professionals, this textbook serves as a valuable tool for those seeking to deepen their understanding of data science as an engineering discipline. Its thought-provoking content stimulates intellectual curiosity and caters to readers who desire more than just code or ready-made formulas. The text invites readers to explore beyond conventional viewpoints, offering an alternative perspective that promotes a big-picture view for integrating theory with practice. Suitable for upper undergraduate or graduate-level courses, this book can also benefit practicing engineers and scientists in various disciplines by enhancing their understanding of modeling and improving data measurement effectively.