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Video
Stanford Electrical Engineering Course on Convex Optimization.
 Course related:
 AMA4850 Optimization Methods
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematical optimization Convex functions
 Resource Type:
 Video

Others
Linear programming, mathematical modeling technique in which a linear function is maximized or minimized when subjected to various constraints. This technique has been useful for guiding quantitative decisions in business planning, in industrial engineering, and—to a lesser extent—in the social and physical sciences.
 Course related:
 AAE3009 Operations Research and Computational Analytics in Air Transport Operations
 Subjects:
 Mathematics and Statistics
 Keywords:
 Linear programming
 Resource Type:
 Others

Courseware
This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:
A complete set of Lecture Videos by Professor Gilbert Strang.
Summary Notes for all videos along with suggested readings in Prof. Strang’s textbook Linear Algebra.
Problem Solving Videos on every topic taught by an experienced MIT Recitation Instructor.
Problem Sets to do on your own with Solutions to check your answers against when you’re done.
A selection of Java® Demonstrations to illustrate key concepts.
A full set of Exams with Solutions, including review material to help you prepare.
 Course related:
 AMA1120 Basic Mathematics II
 Subjects:
 Mathematics and Statistics
 Keywords:
 Algebras Linear
 Resource Type:
 Courseware

Video
With calculus well behind us, it's time to enter the next major topic in any study of mathematics. Linear Algebra! The name doesn't sound very intimidating, but there are some pretty abstract concepts in this subject. Let's start nice and easy simply by learning about what this subject covers and some basic terminology.
 Course related:
 COMP4434 Big Data Analytics
 Subjects:
 Mathematics and Statistics
 Keywords:
 Algebras Linear
 Resource Type:
 Video

Others
In these comprehensive video courses, created by Santiago Basulto, you will learn the whole process of data analysis. You'll be reading data from multiple sources (CSV, SQL, Excel), process that data using NumPy and Pandas, and visualize it using Matplotlib and Seaborn, Additionally, we've included a thorough Jupyter Notebook course, and a quick Python reference to refresh your programming skills.
 Course related:
 AMA1600 Fundamentals of AI and Data Analytics and AMA1751 Linear Algebra
 Subjects:
 Mathematics and Statistics and Computing
 Keywords:
 Computer programming Computer science Python (Computer program language)
 Resource Type:
 Others

Others
We offer mathematics in an enjoyable and easytolearn manner, because we believe that mathematics is fun.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics
 Resource Type:
 Others

Video
Lecture videos from Gilbert Strang's course on Linear Algebra at MIT.
 Course related:
 AMA1120 Basic Mathematics II  Calculus and Linear Algebra
 Subjects:
 Mathematics and Statistics
 Keywords:
 Algebras Linear
 Resource Type:
 Video

Video
This course is an introduction to game theory and strategic thinking. Ideas such as dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling are discussed and applied to games played in class and to examples drawn from economics, politics, the movies, and elsewhere.
 Subjects:
 Mathematics and Statistics and Economics
 Keywords:
 Game theory
 Resource Type:
 Video

Video
Before the advent of computers around 1950, optimization centered either on smalldimensional problems solved by looking at zeroes of first derivatives and signs of second derivatives, or on infinitedimensional problems about curves and surfaces. In both cases, "variations" were employed to understand how a local solution might be characterized. Computers changed the picture by opening the possibility of solving largescale problems involving inequalities, instead of only equations. Inequalities had to be recognized as important because the decisions to be optimized were constrained by the need to respect many upper or lower bounds on their feasibility. A new kind of mathematical analysis, beyond traditional calculus, had to be developed to address these needs. It built first on appealing to the convexity of sets and functions, but went on to amazingly broad and successful concepts of variational geometry, subgradients, subderivatives, and variational convergence beyond just that. This talk will explain these revolutionary developments and why there were essential.
Event date: 1/11/2022
Speaker: Prof. Terry Rockafellar (University of Washington)
Hosted by: Department of Applied Mathematics
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematical optimization Computer science  Mathematics Convex sets Convex functions
 Resource Type:
 Video

Video
Adaptive computation is of great importance in numerical simulations. The ideas for adaptive computations can be dated back to adaptive finite element methods in 1970s. In this talk, we shall first review some recent development for adaptive methods with some application. Then, we will propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FIPINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared with the neural network approximation obtained with uniformly distributed collocation points, the proposed algorithms can significantly improve the accuracy, especially for low regularity and highdimensional problems.
Event date: 18/10/2022
Speaker: Prof. Tao Tang (Beijing Normal UniversityHong Kong Baptist University United International College)
Hosted by: Department of Applied Mathematics
 Subjects:
 Mathematics and Statistics
 Keywords:
 Adaptive computing systems Mathematical models Sampling (Statistics) Differential equations Partial  Numerical solutions
 Resource Type:
 Video

Video
Convex Matrix Optimization (MOP) arises in a wide variety of applications. The last three decades have seen dramatic advances in the theory and practice of matrix optimization because of its extremely powerful modeling capability. In particular, semidefinite programming (SP) and its generalizations have been widely used to model problems in applications such as combinatorial and polynomial optimization, covariance matrix estimation, matrix completion and sensor network localization. The first part of the talk will describe the primaldual interiorpoint methods (IPMs) implemented in SDPT3 for solving medium scale SP, followed by inexact IPMs (with linear systems solved by iterative solvers) for large scale SDP and discussions on their inherent limitations. The second part will present algorithmic advances for solving large scale SDP based on the proximalpoint or augmented Lagrangian framework In particular, we describe the design and implementation of an augmented Lagrangian based method (called SDPNAL+) for solving SDP problems with large number of linear constraints. The last part of the talk will focus on recent advances on using a combination of local search methods and convex lifting to solve lowrank factorization models of SP problems.
Event date: 11/10/2022
Speaker: Prof. KimChuan Toh (National University of Singapore)
Hosted by: Department of Applied Mathematics
 Subjects:
 Mathematics and Statistics
 Keywords:
 Convex programming Semidefinite programming
 Resource Type:
 Video

Video
We introduce a DimensionReduced SecondOrder Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trustregionlike framework, our method preserves the convergence of the secondorder method while using only Hessianvector products in two directions. Moreover; the computational overhead remains comparable to the firstorder such as the gradient descent method. We show that the method has a local superlinear convergence and a global convergence rate of 0(∈3/2) to satisfy the firstorder and secondorder conditions under a commonly used approximated Hessian assumption. We further show that this assumption can be removed if we perform one step of the Krylov subspace method at the end of the algorithm, which makes DRSOM the first firstordertype algorithm to achieve this complexity bound. The applicability and performance of DRSOM are exhibited by various computational experiments in logistic regression, L2Lp minimization, sensor network localization, neural network training, and policy optimization in reinforcement learning. For neural networks, our preliminary implementation seems to gain computational advantages in terms of training accuracy and iteration complexity over stateoftheart firstorder methods including SGD and ADAM. For policy optimization, our experiments show that DRSOM compares favorably with popular policy gradient methods in terms of the effectiveness and robustness.
Event date: 19/09/2022
Speaker: Prof. Yinyu Ye (Stanford University)
Hosted by: Department of Applied Mathematics
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematical optimization Convex programming Nonconvex programming
 Resource Type:
 Video

Video
In a lively show, mathemagician Arthur Benjamin races a team of calculators to figure out 3digit squares, solves another massive mental equation and guesses a few birthdays. How does he do it? He’ll tell you.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mental arithmetic Mental calculators
 Resource Type:
 Video

Video
By analyzing raw data on violent incidents in the Iraq war and others, Sean Gourley and his team claim to have found a surprisingly strong mathematical relationship linking the fatality and frequency of attacks.
 Subjects:
 Mathematics and Statistics
 Keywords:
 War  Mathematical models
 Resource Type:
 Video

Video
Today's math curriculum is teaching students to expect  and excel at  paintbynumbers classwork, robbing kids of a skill more important than solving problems: formulating them. Dan Meyer shows classroomtested math exercises that prompt students to stop and think.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics  Study teaching
 Resource Type:
 Video

Video
What can mathematics say about history? According to TED Fellow JeanBaptiste Michel, quite a lot. From changes to language to the deadliness of wars, he shows how digitized history is just starting to reveal deep underlying patterns.
 Subjects:
 Mathematics and Statistics
 Keywords:
 History  Mathematical models
 Resource Type:
 Video

Video
Having trouble remembering the order of operations? Let's raise the stakes a little bit. What if the future of your (theoretical) kingdom depended on it? Garth Sundem creates a world in which PEMDAS is the hero but only heroic when in the proper order.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Games in mathematics education Games  Mathematics
 Resource Type:
 Video

Video
What's so special about Leonardo da Vinci's Vitruvian Man? With arms outstretched, the man fills the irreconcilable spaces of a circle and a square  symbolizing the Renaissanceera belief in the mutable nature of humankind. James Earle explains the geometric, religious and philosophical significance of this deceptively simple drawing.
 Subjects:
 History and Mathematics and Statistics
 Keywords:
 Mathematics  Social aspects Vitruvian man (Leonardo da Vinci)
 Resource Type:
 Video

Video
Finding the right mate is no cakewalk  but is it even mathematically likely? In a charming talk, mathematician Hannah Fry shows patterns in how we look for love, and gives her top three tips (verified by math!) for finding that special someone.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematical statistics Online dating
 Resource Type:
 Video

Video
With humor and charm, mathematician Eduardo Sáenz de Cabezón answers a question that's wracked the brains of bored students the world over: What is math for? He shows the beauty of math as the backbone of science — and shows that theorems, not diamonds, are forever. In Spanish, with English subtitles.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics
 Resource Type:
 Video

Video
Jim Simons was a mathematician and cryptographer who realized: the complex math he used to break codes could help explain patterns in the world of finance. Billions later, he's working to support the next generation of math teachers and scholars. TED's Chris Anderson sits down with Simons to talk about his extraordinary life in numbers.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Stocks  Mathematical models Simons James Harris Mathematics  Study teaching
 Resource Type:
 Video

Video
Pascal's triangle, which at first may just look like a neatly arranged stack of numbers, is actually a mathematical treasure trove. But what about it has so intrigued mathematicians the world over? Wajdi Mohamed Ratemi shows how Pascal's triangle is full of patterns and secrets.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Pascal's triangle
 Resource Type:
 Video

Video
Hidden truths permeate our world; they're inaccessible to our senses, but math allows us to go beyond our intuition to uncover their mysteries. In this survey of mathematical breakthroughs, Fields Medal winner Cédric Villani speaks to the thrill of discovery and details the sometimes perplexing life of a mathematician. "Beautiful mathematical explanations are not only for our pleasure," he says. "They change our vision of the world."
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics
 Resource Type:
 Video

Video
Unlock the mysteries and inner workings of the world through one of the most imaginative art forms ever  mathematics  with Roger Antonsen, as he explains how a slight change in perspective can reveal patterns, numbers and formulas as the gateways to empathy and understanding.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics
 Resource Type:
 Video

Video
What if we looked at Parkinson's as an neurological electrical problem? Brain researcher Eleftheria Pissadaki and her team study dopamine neurons, the neurons that selectively die during Parkinson's. They discovered that the bigger a neuron is, the more vulnerable it becomes because it simply requires more energy. This new insight is reframing the disease  and by "finding the fuse box for each neuron" and figuring out how much energy it needs, may help us neuroprotect our brain cells.
 Subjects:
 Health Sciences and Mathematics and Statistics
 Keywords:
 Brain  Diseases  Research Brain  Mathematical models
 Resource Type:
 Video

Video
Irina Kareva translates biology into mathematics and vice versa. She writes mathematical models that describe the dynamics of cancer, with the goal of developing new drugs that target tumors. "The power and beauty of mathematical modeling lies in the fact that it makes you formalize, in a very rigorous way, what we think we know," Kareva says. "It can help guide us to where we should keep looking, and where there may be a dead end." It all comes down to asking the right question and translating it to the right equation, and back.
 Subjects:
 Health Sciences and Mathematics and Statistics
 Keywords:
 Cancer  Mathematical models Cancer cells  Mathematical models
 Resource Type:
 Video

Video
How do we make sense of a world that doesn't? By looking in unexpected places, says mathematician Eugenia Cheng. She explains how applying concepts from abstract mathematics to daily life can lead us to a deeper understanding of things like the root of anger and the function of privilege. Learn more about how this surprising tool can help us to empathize with each other.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics  Social aspects Equality
 Resource Type:
 Video

Video
When Nicolas Bourbaki applied to the American Mathematical Society in the 1950s, he was already one of the most influential mathematicians of his time. He'd published articles in international journals and his textbooks were required reading. Yet his application was firmly rejected for one simple reason: Nicolas Bourbaki did not exist. How is that possible? Pratik Aghor digs into the mystery.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics  History Bourbaki Nicolas Functions
 Resource Type:
 Video

Video
Consider the following sentence: "This statement is false." Is that true? If so, that would make the statement false. But if it's false, then the statement is true. This sentence creates an unsolvable paradox; if it's not true and it's not false– what is it? This question led a logician to a discovery that would change mathematics forever. Marcus du Sautoy digs into Gödel's Incompleteness Theorem.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Incompleteness theorems Gödel's theorem
 Resource Type:
 Video

Video
Throughout his life, Hrabowski has loved the intersection of math and language. The challenge of finding clear, simple language to explain complex math problems to others is part of what drove his decision to focus on teaching math. Hrabowski points out that math and statistics provide the tools for not only for engineers and scientists to do their work, but also for physicians, accountants, social scientists, business owners and even university administrators!
 Subjects:
 Mathematics and Statistics
 Keywords:
 Applied mathematics
 Resource Type:
 Video

Video
Robert Lang is a pioneer of the newest kind of origami  using math and engineering principles to fold mindblowingly intricate designs that are beautiful and, sometimes, very useful.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Origami  Mathematics
 Resource Type:
 Video

Video
Margaret Wertheim leads a project to recreate the creatures of the coral reefs using a crochet technique invented by a mathematician  celebrating the amazements of the reef, and deepdiving into the hyperbolic geometry underlying coral creation.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Crocheting Coral reef ecology
 Resource Type:
 Video

Video
From rockets to stock markets, many of humanity's most thrilling creations are powered by math. So why do kids lose interest in it? Conrad Wolfram says the part of math we teach  calculation by hand  isn't just tedious, it's mostly irrelevant to real mathematics and the real world. He presents his radical idea: teaching kids math through computer programming.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics  Study teaching
 Resource Type:
 Video

Video
Physicist Geoffrey West has found that simple, mathematical laws govern the properties of cities  that wealth, crime rate, walking speed and many other aspects of a city can be deduced from a single number: the city's population. In this mindbending talk from TEDGlobal he shows how it works and how similar laws hold for organisms and corporations.
 Subjects:
 Environmental Engineering and Mathematics and Statistics
 Keywords:
 Cities towns  Growth  Econometric models Sustainable urban development
 Resource Type:
 Video

Video
Scott Rickard set out to engineer the ugliest possible piece of music, devoid of repetition, using a mathematical concept known as the Costas Array. In this surprisingly entertaining talk, he shares the math behind musical beauty ... and its opposite.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Repetition in music Mathematics Composition (Music)
 Resource Type:
 Video

Video
When two people join a dating website they are matched according to shared interests and how they answer a number of personal questions. But how do sites calculate the likelihood of a successful relationship? Christian Rudder one of the founders of popular dating site OKCupid details the algorithm behind 'hitting it off.'
 Subjects:
 Computing and Mathematics and Statistics
 Keywords:
 Dating services Computer algorithms Online dating
 Resource Type:
 Video

Video
Would mathematics exist if people didn't? Did we create mathematical concepts to help us understand the world around us, or is math the native language of the universe itself? Jeff Dekofsky traces some famous arguments in this ancient and hotly debated question.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics  Philosophy
 Resource Type:
 Video

Video
During the Cold War, Soviet educators were tasked with raising citizens who could outinnovate and outbuild their American counterparts. One of their primary tools for doing so? Math. Educator Masha Gershman describes how the adaptive, highly social Soviet approach to teaching math can be deployed to prep new generations for an evershifting future.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics  Study teaching
 Resource Type:
 Video

Video
Mohamad Jebara loves mathematics  but he's concerned that too many students grow up thinking that this beautiful, rewarding subject is difficult and boring. His company is experimenting with a bold idea: paying students for completing weekly math homework. He explores the ethics of this model and how it's helping students  and why learning math is crucial in the era of fake news.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics  Study teaching
 Resource Type:
 Video

Video
In this engaging talk, high school math teacher and YouTube star Eddie Woo shares his passion for mathematics, calling it an extra sense that we can all access. Using realworld examples of geometry, he encourages everyone to seek out the patterns around them for "a whole new way to see the world."
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics
 Resource Type:
 Video

Video
Mathematics is not about following rules, it's about playing—and exploring, fighting, looking for clues, and sometimes even breaking things, according to Dan Finkel. In this playful, inspiring talk, the founder of Math for Love offers teachers and parents alike a fivestep guide to sharing the beauty and playfulness of mathematical thinking with children.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics  Study teaching
 Resource Type:
 Video

Video
Origami, which literally translates to "folding paper," is a Japanese practice dating back to at least the 17th century. In origami, a single, traditionally square sheet of paper can be transformed into almost any shape, purely by folding. The same simple concepts yield everything from a paper crane with about 20 steps, to a dragon with over 1,000 steps. Evan Zodl explores the ancient art form.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Origami  Mathematics
 Resource Type:
 Video

Video
The concepts behind linear regression, fitting a line to data with least squares and Rsquared, are pretty darn simple, so let's get down to it
 Course related:
 BRE366 Analytical Skills and Methods (Quantitative Research Methods)
 Subjects:
 Mathematics and Statistics
 Keywords:
 Regression analysis R (Computer program language)
 Resource Type:
 Video

Others
Fuzzy Logic Toolbox™ provides MATLAB® functions, apps, and a Simulink® block for analyzing, designing, and simulating systems based on fuzzy logic. The product guides you through the steps of designing fuzzy inference systems. Functions are provided for many common methods, including fuzzy clustering and adaptive neurofuzzy learning. The toolbox lets you model complex system behaviors using simple logic rules, and then implement these rules in a fuzzy inference system. You can use it as a standalone fuzzy inference engine. Alternatively, you can use fuzzy inference blocks in Simulink and simulate the fuzzy systems within a comprehensive model of the entire dynamic system.
 Course related:
 SD5804 Design Research Methods
 Subjects:
 Computing and Mathematics and Statistics
 Keywords:
 Fuzzy systems Fuzzy logic
 Resource Type:
 Others

Video
This channel contains a complete list of physics videos, as well as hundreds of chemistry, astronomy, math, and mechanical engineering videos. The physics videos explain the fundamental concepts of physics with some easy to follow examples on how to solve physics problems. The chemistry videos cover all the basic topics of chemistry, the astronomy videos explain the wonders of Earth and our Universe, and the math videos cover many topics in algebra, trigonometry, precalculus, calculus and differential equations.
 Subjects:
 Mechanical Engineering, Cosmology and Astronomy, Electrical Engineering, Chemistry, Mathematics and Statistics, and Physics
 Keywords:
 Mechanical engineering Physics Mathematics Kalman filtering Chemistry Electrical engineering Astronomy
 Resource Type:
 Video

Video
課程簡介：微分表切線斜率，積分表曲線下圍出的面積，兩截然不同的東西透過微積分基本定理連結在一起。
 Course related:
 AMA1007 Calculus and Linear Algebra
 Subjects:
 Mathematics and Statistics
 Keywords:
 Calculus
 Resource Type:
 Video

ejournal
In this journal platform, you can find the articles which published under the Creative Commons AttributionNonCommercial 4.0 International License. The journal covers a various disciplines, including:
Biomedical & Life Sciences
Business & Management
Chemistry & Material Science
Computer & Communications
Earth & Environmental Science
Engineering
Humanities
Physics & Mathematics
Social Sciences
 Subjects:
 Management, Physics, Chemistry, Computing, Mathematics and Statistics, Biology, and Environmental Sciences
 Keywords:
 Industrial management Computer science Management Physics Mathematics Social Sciences Chemistry Engineering Environmental sciences Humanities Biology
 Resource Type:
 ejournal

ejournal
Maxwell Scientific Publication Corp. operates as an independent science and technology publisher with a global reputation for quality products and services to contribute to the advancement of research knowledge. In this journal platform, you can find the articles which published under the open license. The journal including the disciplines:
Agricultural Sciences
Business Management & Economics Computer & Information Technology
Engineering
Food Science and Technology
Mathematics
Medicines
Social Sciences
 Subjects:
 Health Sciences, Environmental Sciences, Physics, Economics, Chemistry, Computing, Mathematics and Statistics, Biology, Management, Medicine, and Food Science
 Keywords:
 Statistics Science Periodicals Industrial management Food science Agriculture Fisheries Medicine Mathematics Life sciences Economics Technology Dairying Social sciences Environmental sciences Engineering Aquatic sciences Information technology Food industry trade
 Resource Type:
 ejournal

ejournal
In this journal platform, you can find the articles which published under the open license. The journal including the disciplines:
Biomedical & Life Science
Business & Economics
Chemistry & Materials Science
Computer Science & Communication
Earth & Environmental Science
Engineering
Medicine & Healthcare
Physics & Mathematics
Social Science & Humanities
 Subjects:
 Health Sciences, Environmental Sciences, Physics, Economics, Chemistry, Computing, Mathematics and Statistics, and Biology
 Keywords:
 Science Periodicals Industrial management Computer science Physics Mathematics Life sciences Economics Technology Chemistry Social sciences Environmental sciences Engineering Materials science Medicine
 Resource Type:
 ejournal

ejournal
In this journal platform, you can find the articles which published under the open license. The journal including the disciplines:
Biological Sciences
Medicine
Case Reports
Physical Sciences
Social Sciences and Education
Mathematics, Engineering, and Computer Science
 Subjects:
 Medicine, Chemistry, Computing, Mathematics and Statistics, Biology, and Physics
 Keywords:
 Science Periodicals Computer science Physics Mathematics Education Technology Social sciences Environmental sciences Engineering Biology Medicine Physical sciences
 Resource Type:
 ejournal

ejournal
Estonian Academy Publishers issues seven open access scientific journals, peerreviewed, indexed and abstracted in international review publications and databases. All journals have an international Editorial board. Publications of the Estonian Academy Publishers cover almost all important areas of contemporary science. Our journals are peer reviewed and recognized by the Estonian Research Council and the Estonian Committee of Science Compentence as journals meeting international scientific standards.
 Subjects:
 Environmental Sciences, Physics, Chemistry, Archeology, Mathematics and Statistics, Biology, and Foreign Language Learning
 Keywords:
 Science Periodicals Uralic languages Ecology Mathematics Archaeology Technology Chemistry Social sciences Europe  Baltic Sea Region Engineering Humanities Geology History Physics
 Resource Type:
 ejournal

ebook
"This textbook is aligned with the British Columbia Adult Basic Education learning outcomes for Mathematics: Intermediate Level Algebra. The textbook introduces the fundamental concepts of algebra, geometry, and trigonometry while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. This text was adapted from Elementary Algebra and Prealgebra, textbooks originally published by OpenStax."BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Algebra Textbooks Functions
 Resource Type:
 ebook

ebook
"We are often faced with questions concerning our finances: Am I saving enough to put my daughter through college? How much will my investment be worth five years from now? Should I pay down my mortgage with weekly or monthly payments? The mathematics of finance allows us to answer these and similar questions. This textbook aligns with Adult Basic Education (ABE) Advanced Level Mathematics"BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Business mathematics Mathematics Textbooks
 Resource Type:
 ebook

ebook
"This resource covers the following learning objectives: explain the uses and misuses of statistics
 Subjects:
 Mathematics and Statistics
 Keywords:
 Statistics Mathematical statistics
 Resource Type:
 ebook

ebook
"This book is a polished version of the author's notes for a course entitled Several Complex Variables. It should be suitable for a semesterlong topics course or for selfstudy as an introduction to the subject. The prerequisites are decent knowledge of vector calculus, basic real analysis, and a working knowledge of complex analysis in one variable. It should be accessible to beginning graduate students after a complex analysis course, and perhaps even very advanced undergraduates. This is enough material for a semesterlong course, including quite a few exercises sprinkled throughout the text, all of which the reader should at least be attempting. It is not meant as an exhaustive reference, but simply as a whirlwind tour of several complex variables"BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Textbooks Functions of complex variables
 Resource Type:
 ebook

ebook
"This book is a continuation of Basic Analysis: Introduction to Real Analysis  Volume 1. Volume II continues into multivariable analysis, starting with differential calculus, including inverse and implicit function theorems, continuing with differentiation under the integral and path integrals, which are often not covered in a course like this, and multivariable Riemann integral. Finally, there is also a chapter on power series, ArzelàAscoli, StoneWeierstrass, and Fourier series. Together, the two volumes provide enough material for several different types of yearlong sequences. A student who absorbs the first volume and the first three chapters of volume II should be more than prepared for real and complex analysis courses at the graduate level"BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Functions of real variables Mathematical analysis
 Resource Type:
 ebook

ebook
"This is a course in undergraduate real analysis, also known as advanced calculus. The book works for both basic courses for students who do not necessarily wish to go to graduate school and also more advanced courses that prepare students for graduate study and cover topics such as metric spaces. A prerequisite for the course is a basic proof course. This book starts with analysis on the real line, going through sequences, series, and then into continuity, the derivative, and the Riemann integral using the Darboux approach. There are plenty of available detours along the way, or you can power through toward the metric spaces in chapter 7. The philosophy is that metric spaces are absorbed much better by the students after they have gotten comfortable with basic analysis techniques in the very concrete setting of the real line. As a bonus, the book can be used both by slowerpaced, more concrete courses, as well as a fasterpaced, more abstract courses for future graduate students"BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Functions of real variables Mathematical analysis
 Resource Type:
 ebook

ebook
"Elementary Algebra  2e is designed to meet scope and sequence requirements for a onesemester elementary algebra course. The book's organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty"BC Campus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Algebra Textbooks Functions
 Resource Type:
 ebook

ebook
"The Math for Trades: Volume 1 textbook represents the building blocks for math training. The book includes whole numbers, fractions, decimals, and percents. The material is presented from a trades perspective with easytounderstand examples and video explanations accompanying questions. The goal of this volume is to get students prepared for the more advanced topics that they will encounter during their trades math education"BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics
 Resource Type:
 ebook

ebook
"This textbook is intended for adult learners who wish to review and improve their algebra skills. The content covers all the ABE outcomes for the Algebraic Math  Advanced Level. The concepts are explained concisely, but with enough depth to provide students with the background necessary for success in college or university level mathematics. The ample number of examples and exercises makes this text a great resource for students as well as for instructors"BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Trigonometry Algebra Textbooks
 Resource Type:
 ebook

ebook
"This text was written for a collegelevel liberal arts math class. It addresses math concepts that most people will encourter as part of their everyday life, including statistics, probablility, growth, finance, graph theory, voting systems, fair division, apportionment, and geometric symmetry and the golden ratio. Each chapter includes a set of homework questions for practice"BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics Social sciences  Mathematics
 Resource Type:
 ebook

ebook
"This textbook is a concise, understandable, and effective guide on intermediate level mathematics. This book can be used by Adult Basic Education programs at colleges
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics Textbooks
 Resource Type:
 ebook

ebook
"Combinatorics provides an introduction to enumeration, graph theory, and design theory. It is aimed at upperlevel undergraduate students and the exercises expect some mathematical sophistication, including a reasonable ability to construct proofs. The text is designed to be used in an undergraduate course, but could be suitable for independent study by a student with some mathematical background and understanding of proofs. It does not assume any background knowledge of combinatorics"BC Campus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Combinatorial analysis  Textbooks
 Resource Type:
 ebook

ebook
"Calculus arose as a tool for solving practical scientific problems through the centuries. However, it is often taught as a technical subject with rules and formulas (and occasionally theorems), devoid of its connection to applications. In this textbook, the applications form an important focal point, with emphasis on life sciences. This places the techniques and concepts into practical context, as well as motivating quantitative approaches to biology taught to undergraduates. While many of the examples have a biological flavour, the level of biology needed to understand those examples is kept at a minimum. The problems are motivated with enough detail to follow the assumptions, but are simplified for the purpose of pedagogy"BC Campus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Life sciences Differential calculus Textbooks
 Resource Type:
 ebook

ebook
"In 2013, Lyryx forked the nowpopular Calculus open textbook written by David Guichard. Michael Cavers of the University of Calgary, together with the Lyryx editorial team, further redeveloped the content, examples, diagrams, and overall lookandfeel of the book, making it more accessible to first year college and university students. Additional contributors have helped improve the content, including Mark Blenkinsop of Carleton University. In particular, there was the addition of an introductory chapter reviewing the fundamental topics required in a first semester Calculus course, and the paring down of topics that are typically beyond the scope of math and engineering service courses. Currently, the book covers the standard Calculus I and II courses, with Calculus III under development."Open Textbook Library.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Calculus Textbooks
 Resource Type:
 ebook

ebook
"Essential skills are used in every job to varying degrees and at different levels of complexity. They provide the foundation for learning all other skills and enable people to evolve in their jobs and adapt to changes in the workplace. The following list of lines and competencies was generated with the goal of creating an entrylevel trades training resource, while still offering the flexibility for lines to be used as standalone books"BC Campus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics Textbooks Geometry
 Resource Type:
 ebook

ebook
"Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra. In writing this book I have been guided by the these principles: An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student's place, and have chosen to err on the side of too much detail rather than not enough. An elementary text can't be better than its exercises. This text includes 2041 numbered exercises, many with several parts. They range in difficulty from routine to very challenging. An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and defonitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 299 completely worked out examples. Where appropriate, concepts and results are depicted in 188 figures."BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential equations Textbooks
 Resource Type:
 ebook

ebook
"Introductory Business Statistics provides students with an intuitive understanding of sampling distributions and their place in hypothesis testing. This texts aims to help students understand how statistics works, not just how to "get the right number"."BCcampus website.
 Subjects:
 Management and Mathematics and Statistics
 Keywords:
 Commercial statistics Textbooks
 Resource Type:
 ebook

ebook
"This is a textbook for first year Computer Science. Algorithms and Data Structures With Applications to Graphics and Geometry."BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Data structures (Computer science) Textbooks Algorithms
 Resource Type:
 ebook

ebook
"Precalculus (was College Algebra) is an introductory text. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are openended). Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. Note: this book was updated on the BC Open textbook Project site on February, 17, 2015 to include the version of the textbook with chapters on Trigonometry."BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Precalculus Textbooks
 Resource Type:
 ebook

ebook
"This book is meant to be a textbook for a standard onesemester introductory statistics course for general education students.Over time the core content of this course has developed into a welldefined body of material that is substantial for a onesemester course. The authors believe that the students in this course are best served by a focus on the core material and not by an exposure to a plethora of peripheral topics. Therefore in writing this book we have sought to present material that comprises fully a central body of knowledge that is defined according to convention, realistic expectation with respect to course duration and students' maturity level, and our professional judgment and experience."BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Statistics Textbooks
 Resource Type:
 ebook

Video
In 44 episodes, Adriene Hill teaches you Statistics! This course is based on the 2018 AP Statistics curriculum and introduces everything from basic descriptive statistics to data collection to hot topics in data analysis like Big Data and neural networks. By the end of the course, you will be able to: *Identify questions that can be answered using statistics *Describe patterns, trends, associations, and relationships in data both numerically and graphically *Justify a conclusion using evidence from data, definitions, or statistical inference *Apply statistical models to make inferences and predictions from data sets *Understand how statistics are used broadly in the world and interpret their meaning, like in newspapers or scientific studies Learning playlist
 Subjects:
 Mathematics and Statistics
 Keywords:
 Statistics
 Resource Type:
 Video

Others
Numerical methods are techniques to approximate mathematical procedures (e.g., integrals). Approximations are needed because we either cannot solve the procedure analytically (e.g., the standard normal cumulative distribution function) or because the analytical method is intractable (e.g., solving a set of a thousand simultaneous linear equations for a thousand unknowns). By end of this course, participants will be able to apply the numerical methods for the following mathematical procedures and topics: differentiation, nonlinear equations, and simultaneous linear equations, interpolation, regression, integration, and ordinary differential equations. Additionally, they will be able to calculate errors and implement their relationship to the accuracy of the numerical solutions. To be prepared for this course, students should have a passing grade in introductory physics, integral calculus, differential calculus, and ordinary differential equations.
 Course related:
 BSE3302 Computer Methods in Building Services Engineering
 Subjects:
 Mathematics and Statistics
 Keywords:
 Numerical analysis Numerical calculations
 Resource Type:
 Others

Video
This video playlist covers the topic of: 1. PDE 1  Introduction 2.PDE 2  Three fundamental examples 3.PDE 3  Transport equation: derivation 4.PDE 4  Transport equation: general solution 5. PDE 5  Method of characteristics 6. PDE 6  Transport with decay and nonlinear transport 7.PDE 7  Wave equation: intuition 8.PDE 8  Wave equation: derivation 9.PDE 9  Wave equation: general solution 10.PDE 10  Wave equation: d'Alembert's formula 11.PDE 11  Wave equation: d'Alembert examples 12.PDE 12  Wave equation: characteristics 13.PDE 13  Wave equation: separation of variables 14.FA 1  Fourier series introduction 15.FA 2  Computing Fourier series 16.PDE  Heat equation: intuition 17.PDE  Finite differences: introduction
 Course related:
 AMA3723 Further Mathematical Methods for Finance
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential equations Partial
 Resource Type:
 Video

Video
In this video produced at The University of Manchester in 1972 the eminent Cornelius Lanczos is interviewed on his contributions to applied mathematics. Copyright by The University of Manchester.
 Course related:
 AMA613 Mathematics Seminar and ELC6001 Presentation Skills for Research Students
 Subjects:
 Mathematics and Statistics
 Keywords:
 Interviews Lanczos Cornelius 18931974
 Resource Type:
 Video

Others
Nicholas John Higham FRS is a British numerical analyst. He is Royal Society Research Professor and Richardson Professor of Applied Mathematics in the School of Mathematics at the University of Manchester. In this blog, it covers the popular topic, such as: (1) Top 5 Beamer Tips (2) The Nearest Correlation Matrix (3) The Top 10 Algorithms in Applied Mathematics (4) A Black Background for More Restful PDF viewing (5) Typesetting Mathematics According to the ISO Standard (6) Fourth Edition (2013) of Golub and Van Loan’s Matrix Computations (7) The Rise of Mixed Precision Arithmetic (8) Second Edition (2013) of Matrix Analysis by Horn and Johnson (9) Half Precision Arithmetic: fp16 Versus bfloat16 (10) Managing BibTeX Files with Emacs (11) Five Examples of Proofreading (12) Implicit Expansion: A Powerful New Feature of MATLAB R2016b (13) Dot Grid Paper for Writing Mathematics (14) Programming Languages: An Applied Mathematics View (15) Three BibTeX Tips (16) Better LaTeX Tables with Booktabs (17) The Princeton Companion to Applied Mathematics (18) Numerical Methods That (Usually) Work (19) What’s New in MATLAB R2017a? (20) What Is Numerical Stability?
 Course related:
 AMA615 Nonlinear Optimization Methods and AMA611 Applied Analysis
 Subjects:
 Mathematics and Statistics
 Keywords:
 Computer programming Numerical analysis
 Resource Type:
 Others

Video
This video presents an overview of the Fourier Transform, which is one of the most important transformations in all of mathematical physics and engineering. This series will introduce the analytic theory of the Fourier Transform, along with the Fast Fourier Transform (FFT) algorithm for efficient computations. We will explore lots of applications in image compression, audio analysis, and solving partial differential equations.
 Course related:
 EIE4413 Digital Signal Processing, EIE3331 Communication Fundamentals, and EE3312 Linear Systems
 Subjects:
 Mathematics and Statistics
 Keywords:
 Fourier transformations
 Resource Type:
 Video

Video
Professor Strang describes independent vectors and the column space of a matrix as a good starting point for learning linear algebra. His outline develops the five shorthand descriptions of key chapters of linear algebra.
 Course related:
 COMP4432 Machine Learning
 Subjects:
 Mathematics and Statistics
 Keywords:
 Algebras Linear
 Resource Type:
 Video

Video
Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilondelta definition of limits.
 Course related:
 AMA1110 Basic Mathematics I – Calculus and Probability & Statistics and BRE2031 Environmental Science
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential calculus
 Resource Type:
 Video

Others
This sequence is ideal for students or early data science professionals who want to strengthen their knowledge of fundamental probability and statistics concepts. Mastery of Mathematical Fundamentals is a prerequisite.
 Course related:
 AMA1110 Basic Mathematics I – Calculus and Probability & Statistics
 Subjects:
 Finance and Mathematics and Statistics
 Keywords:
 Probabilities Mathematical statistics Business mathematics
 Resource Type:
 Others

Video
In this lecture, we consider strategies for adversarial games such as chess. We discuss the minimax algorithm, and how alphabeta pruning improves its efficiency. We then examine progressive deepening, which ensures that some answer is always available.
 Course related:
 COMP4431 Artificial Intelligence
 Subjects:
 Computing and Mathematics and Statistics
 Keywords:
 Artificial intelligence
 Resource Type:
 Video

Others
This learning material covers the topic of differentiation by considering first principles (gradients of chords and tangents).
 Course related:
 AMA1110 Basic Mathematics I – Calculus and Probability & Statistics
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential calculus
 Resource Type:
 Others

Video
An example of using least squares to do data fitting. In this example, we demonstrate how to 1) fit a straight line using ordinary leastsquares method, and 2) estimate value of a new input based on the fitted line.
 Course related:
 LSGI3242A Digital Terrain Modelling
 Subjects:
 Computing and Mathematics and Statistics
 Keywords:
 Least squares Regression analysis
 Resource Type:
 Video

MOOC
Why do we study statistics? The field of statistics provides professionals and scientists withconceptual foundations and useful techniques for evaluating ideas, testing theories, and  ultimately uncovering the truth in any situation. This course will familiarize you with data and basic statistical concepts, enabling you to analyze data using graphs and statistics. We'll start with types of data, controlled experiments,and observational study. You'll learn touse ahistogram, a representation of the distribution of numerical data, to easily arrange data. You will learn about basic concepts of statistics, such as average and standard deviation. Methods of using the normal approximation to solve a problem will be covered in this course. Inaddition, we'll discussthe correlation coefficient and the regression method in order to represent the relationship between two variables.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Statistics
 Resource Type:
 MOOC

Courseware
Probability and statistics help to bring logic to a world replete with randomness and uncertainty. This course will give you the tools needed to understand data, science, philosophy, engineering, economics, and finance. You will learn not only how to solve challenging technical problems, but also how you can apply those solutions in everyday life.With examples ranging from medical testing to sports prediction, you will gain a strong foundation for the study of statistical inference, stochastic processes, randomized algorithms, and other subjects where probability is needed.
 Course related:
 AMA1501 Introduction to Statistics in Business
 Subjects:
 Mathematics and Statistics
 Keywords:
 Probabilities
 Resource Type:
 Courseware

ebook
This book is not intended for budding mathematicians. It was created for a math program in which most of the students in upperlevel math classes are planning to become secondary school teachers. For such students, conventional abstract algebra texts are practically incomprehensible, both in style and in content. Faced with this situation, we decided to create a book that our students could actually read for themselves. In this way we have been able to dedicate class time to problemsolving and personal interaction rather than rehashing the same material in lecture format.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Algebra Abstract Textbooks
 Resource Type:
 ebook

ebook
Open Resources for Community College Algebra (ORCCA) is an opensource, openlylicensed textbook package (eBook, print, and online homework) for basic and intermediate algebra. At Portland Community College, Part 1 is used in MTH 60, Part 2 is used in MTH 65, and Part 3 is used in MTH 95.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Algebra Textbooks
 Resource Type:
 ebook

ebook
This book consists of ten weeks of material given as a course on ordinary differential equations (ODEs) for second year mathematics majors at the University of Bristol. It is the first course devoted solely to differential equations that these students will take. This book consists of 10 chapters, and the course is 12 weeks long. Each chapter is covered in a week, and in the remaining two weeks I summarize the entire course, answer lots of questions, and prepare the students for the exam. I do not cover the material in the appendices in the lectures. Some of it is basic material that the students have already seen that I include for completeness and other topics are "tasters" for more advanced material that students will encounter in later courses or in their project work. Students are very curious about the notion of chaos, and I have included some material in an appendix on that concept. The focus in that appendix is only to connect it with ideas that have been developed in this course related to ODEs and to prepare them for more advanced courses in dynamical systems and ergodic theory that are available in their third and fourth years.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential equations Textbooks Differential equations Partial
 Resource Type:
 ebook

ebook
Introduction to Statistics is a resource for learning and teaching introductory statistics. This work is in the public domain. Therefore, it can be copied and reproduced without limitation. However, we would appreciate a citation where possible. Please cite as: Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University. Instructor's manual, PowerPoint Slides, and additional questions are available.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Statistics Textbooks
 Resource Type:
 ebook

ebook
This free undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. It is designed to be the textbook for a bridge course that introduces undergraduates to abstract mathematics, but it is also suitable for independent study by undergraduates (or mathematically mature highschool students), or for use as a very inexpensive supplement to undergraduate courses in any field of abstract mathematics.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics Textbooks
 Resource Type:
 ebook

ebook
Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. Use of this book will help the student develop the insight and intuition necessary to master algebraic techniques and manipulative skills.Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Algebra Textbooks
 Resource Type:
 ebook

ebook
This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. There are problems that some people will solve quickly, and there are problems that will take days of thought for everyone. Probably the best way to use this book is to work on a problem until you feel you are not making progress and then go on to the next one. Think about the problem you couldn't get as you do other things. The next chance you get, discuss the problem you are stymied on with other members of the class. Often you will all feel you've hit dead ends, but when you begin comparing notes and listening carefully to each other, you will see more than one approach to the problem and be able to make some progress. In fact, after comparing notes you may realize that there is more than one way to interpret the problem. In this case your first step should be to think together about what the problem is actually asking you to do. You may have learned in school that for every problem you are given, there is a method that has already been taught to you, and you are supposed to figure out which method applies and apply it. That is not the case here. Based on some simplified examples, you will discover the method for yourself. Later on, you may recognize a pattern that suggests you should try to use this method again.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Combinatorial analysis Textbooks
 Resource Type:
 ebook

ebook
This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction. The book has been used by the author and several other faculty at Southern Connecticut State University. There are nine chapters and more than enough material for a semester course. Student reviews are favorable. It is written in an informal, conversational style with a large number of interesting examples and exercises, so that a student learns to write proofs while working on engaging problems.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics Textbooks
 Resource Type:
 ebook

ebook
Prior to 1990, the performance of a student in precalculus at the University of Washington was not a predictor of success in calculus. For this reason, the mathematics department set out to create a new course with a specific set of goals in mind: A review of the essential mathematics needed to succeed in calculus. An emphasis on problem solving, the idea being to gain both experience and confidence in working with a particular set of mathematical tools. This text was created to achieve these goals and the 200405 academic year marks the eleventh year in which it has been used. Several thousand students have successfully passed through the course. This book is full of worked out examples. We use the the notation “Soluion.” to indicate where the reasoning for a problem begins; the symbol ?? is used to indicate the end of the solution to a problem. There is a Table of Contents that is useful in helping you find a topic treated earlier in the course. It is also a good rough outline when it comes time to study for the final examination. The book also includes an index at the end. Finally, there is an appendix at the end of the text with ”answers” to most of the problems in the text. It should be emphasized these are ”answers” as opposed to ”solutions”. Any homework problems you may be asked to turn in will require you include all your work; in other words, a detailed solution. Simply writing down the answer from the back of the text would never be sufficient; the answers are intended to be a guide to help insure you are on the right track.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Precalculus Textbooks
 Resource Type:
 ebook

ebook
Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who: have had previous courses in prealgebra wish to meet the prerequisites of higher level courses such as elementary algebra need to review fundamental mathematical concenpts and techniques This text will help the student devlop the insight and intuition necessary to master arithmetic techniques and manipulative skills. It was written with the following main objectives: to provide the student with an understandable and usable source of information to provide the student with the maximum oppurtinity to see that arithmetic concepts and techniques are logically based to instill in the student the understanding and intuitive skills necessary to know how and when to use particular arithmetic concepts in subsequent material cources and nonclassroom situations to give the students the ability to correctly interpret arithmetically obtained results We have tried to meet these objects by presenting material dynamically much the way an instructure might present the material visually in a classroom. (See the development of the concept of addition and subtraction of fractions in section 5.3 for examples) Intuition and understanding are some of the keys to creative thinking, we belive that the material presented in this text will help students realize that mathematics is a creative subject.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics Textbooks
 Resource Type:
 ebook

ebook
This text covers the standard material for a US undergraduate first course: linear systems and Gauss's Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications. It has extensive exercise sets with worked answers to all exercises, including proofs, beamer slides for classroom use, and a lab manual for computer work. The approach is developmental. Although everything is proved, it introduces the material with a great deal of motivation, many computational examples, and exercises that range from routine verifications to a few challenges. Ancillary materials are available at the publisher link.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Textbooks Algebras Linear
 Resource Type:
 ebook

ebook
A First Course in Linear Algebra is an introductory textbook aimed at collegelevel sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finitedimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way. A unique feature of this book is that chapters, sections and theorems are labeled rather than numbered. For example, the chapter on vectors is labeled "Chapter V" and the theorem that elementary matrices are nonsingular is labeled "Theorem EMN." Another feature of this book is that it is designed to integrate SAGE, an open source alternative to mathematics software such as Matlab and Maple. The author includes a 45minute video tutorial on SAGE and teaching linear algebra. This textbook has been used in classes at: Centre for Excellence in Basic Sciences, Westmont College, University of Ottawa, Plymouth State University, University of Puget Sound, University of Notre Dame, Carleton University, Amherst College, Felician College, Southern Connecticut State University, Michigan Technological University, Mount Saint Mary College, University of Western Australia, Moorpark College, Pacific University, Colorado State University, Smith College, Wilbur Wright College, Central Washington U (Lynwood Center), St. Cloud State University, Miramar College, Loyola Marymount University.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Textbooks Algebras Linear
 Resource Type:
 ebook

ebook
Teaching Mathematics is nothing less than a mathematical manifesto. Arising in response to a limited National Curriculum, and engaged with secondary schooling for those aged 11 ̶ 14 (Key Stage 3) in particular, this handbook for teachers will help them broaden and enrich their students’ mathematical education. It avoids specifying how to teach, and focuses instead on the central principles and concepts that need to be borne in mind by all teachers and textbook authors—but which are little appreciated in the UK at present. This study is aimed at anyone who would like to think more deeply about the discipline of ‘elementary mathematics’, in England and Wales and anywhere else. By analysing and supplementing the current curriculum, Teaching Mathematics provides food for thought for all those involved in school mathematics, whether as aspiring teachers or as experienced professionals. It challenges us all to reflect upon what it is that makes secondary school mathematics educationally, culturally, and socially important.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics  Study teaching (Secondary)
 Resource Type:
 ebook

ebook
The pedagogical approach is anchored in formal definitions/proof of security, but in a way that I believe is more accessible than what is "traditional" in crypto. All security definitions are written in a unified and simplified "gamebased" style. For an example of what security definitions look like in this style, see the index of security definitions (which will make more sense after reading chapters 2 & 4).
 Subjects:
 Mathematics and Statistics
 Keywords:
 Textbooks Cryptography
 Resource Type:
 ebook

ebook
This book is written for students who have taken calculus and want to learn what “real mathematics" is. We hope you will find the material engaging and interesting, and that you will be encouraged to learn more advanced mathematics. This is the second edition of our text. It is intended for students who have taken a calculus course, and are interested in learning what higher mathematics is all about. It can be used as a textbook for an "Introduction to Proofs" course, or for selfstudy. Chapter 1: Preliminaries, Chapter 2: Relations, Chapter 3: Proofs, Chapter 4: Principles of Induction, Chapter 5: Limits, Chapter 6: Cardinality, Chapter 7: Divisibility, Chapter 8: The Real Numbers, Chapter 9: Complex Numbers. The last 4 chapters can also be used as independent introductions to four topics in mathematics: Cardinality; Divisibility; Real Numbers; Complex Numbers.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Logic Symbolic mathematical Textbooks
 Resource Type:
 ebook
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