Written in the wake of the advent of Relativity by an author who made important contributions to projective and differential geometry, and topology, this early Cambridge Tract in Mathematics and Theoretical Physics aimed to assist students of the time from the fields of differential geometry and mathematical physics. Beginning by introducing formal preliminaries, the text continues, bringing the underlying differential invariant theory that to this day remains relevant in a range of geometrical and physical applications, to the fore.
Introducing Mathematics traces the story of mathematics from the ancient world to modern times, describing the great discoveries and providing an accessible introduction to topics such as algebra and
This classic undergraduate text acquaints students with the fundamental concepts and methods of mathematics. In addition to introducing many historical figures from the 18th through the mid-20th centu
What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowle
This collection of articles brings together research from around the world on the use of history in teaching mathematics. Some articles present theoretical perspectives on the use of history, while ot
Invigorate instruction and engage students with this updated treasure trove of 114 ready-to-use techniques compiled by two of the greatest minds in mathematics.
Co-written by a professor of education and a Nobel Prize-winning mathematician, this volume presents more than 100 motivational ways to teach key mathematical concepts in secondary school classrooms.
This exciting text for the pre-service elementary teacher provides hands on mathematics lessons they can use to introduce mathematical concepts and skills that students find particularly challenging.
Field Trips and Fund-Raisers: Introducing Fractions is one of five units in the Contexts for Learning Mathematics' Investigating Fractions, Decimals, and Percents (4 - 6) The focus of this unit is th
Yang (U. of Cambridge) offers a graduate or undergraduate textbook introducing algorithms commonly used in computational mathematics and modern scientific computing. It ranges from mathematical founda
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 cha
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 cha
Since the early eighteenth century, the theory of networks and graphs has matured into an indispensable tool for describing countless real-world phenomena. However, the study of large-scale features of a network often requires unrealistic limits, such as taking the network size to infinity or assuming a continuum. These asymptotic and analytic approaches can significantly diverge from real or simulated networks when applied at the finite scales of real-world applications. This book offers an approach to overcoming these limitations by introducing operator graph theory, an exact, non-asymptotic set of tools combining graph theory with operator calculus. The book is intended for mathematicians, physicists, and other scientists interested in discrete finite systems and their graph-theoretical description, and in delineating the abstract algebraic structures that characterise such systems. All the necessary background on graph theory and operator calculus is included for readers to underst
Introducing readers to Serres' manner of 'doing philosophy' and follows the path of his novel manner of bearing witness, for which 'mathematical thinking' plays a crucial role throughout his entire oe
Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.
Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.
