Current and Future Perspectives of Ethnomathematics as a Program
This survey on the modernity of ethnomathematics addresses numerous themes related to both ethnomathematics and mathematics education. It offers a broader view of mathematics, including ideas, procedures, concepts, processes, methods, and practices rooted in distinct cultural environments. In addition, by reflecting on the social and political dimensions of ethnomathematics, another important aspect of this research program is the development of innovative approaches for a dynamic and glocalized society
Milton Rosa --- Ubiratan D’Ambrosio --- Daniel Clark Orey --- Lawrence Shirley --- et al.
New Developments in Geometric Function Theory II
This project aimed to gather together the latest developments in research concerning complex-valued functions from the perspective of geometric function theory. Scholars’ contributions were sought on topics including, but not limited to: new classes of univalent and bi-univalent functions; studies regarding coefficient estimates including the Fekete–Szego functional, Hankel determinants, and Toeplitz matrices; applications of different types of operators in geometric function theory including differential, integral,
MDPI - Multidisciplinary Digital Publishing Institute
Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces. Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http://www.aimath.org/textbooks/. This version was created using Mathbook Xml (https://mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at Umass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at Umass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.
Introduction to Financial Mathematics Concepts and Computational Methods
Financial Mathematics Concepts, Computational Methods
Introduction to Financial Mathematics: Concepts and Computational Methods serves as a primer in financial mathematics with a focus on conceptual understanding of models and problem solving. It includes the mathematical background needed for risk management, such as probability theory, optimization, and the like. The goal of the book is to expose the reader to a wide range of basic problems, some of which emphasize analytic ability, some requiring programming techniques and others focusing on statistical data analysis. In addition, it covers some areas which are outside the scope of mainstream financial mathematics textbooks. For example, it presents marginal account setting by the CCP and systemic risk, and a brief overview of the model risk. Inline exercises and examples are included to help students prepare for exams on this book.
Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. The textbook was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. Courses using this textbook have been articulated by the University of California for transfer of credit. The textbook contains full materials for course offerings, including expository text, examples, labs, homework, and projects. A Teacher’s Guide is currently available in print form and on the Connexions site at and supplemental course materials including additional problem sets and video lectures are available. The on-line text for each of these collections collections will meet the Section 508 standards for accessibility. An on-line course based on the textbook was also developed by Illowsky and Dean. It has won an award as the best on-line California community college course. The on-line course will be available at a later date as a collection in Connexions, and each lesson in the on-line course will be linked to the on-line textbook chapter. The on-line course will include, in addition to expository text and examples, videos of course lectures in captioned and non-captioned format. The original preface to the book as written by professors Illowsky and Dean, now follows: This book is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it. The text is named Collaborative Statistics because students learn best by doing. In fact, they learn best by working in small groups. The old saying “two heads are better than one” truly applies here. Our emphasis in this text is on four main concepts: thinking statistically incorporating technology working collaboratively writing thoughtfully These concepts are integral to our course. Students learn the best by actively participating, not by just watching and listening. Teaching should be highly interactive. Students need to be thoroughly engaged in the learning process in order to make sense of statistical concepts. Collaborative Statistics provides techniques for students to write across the curriculum, to collaborate with their peers, to think statistically, and to incorporate technology. This book takes students step by step. The text is interactive. Therefore, students can immediately apply what they read. Once students have completed the process of problem solving, they can tackle interesting and challenging problems relevant to today’s world. The problems require the students to apply their newly found skills. In addition, technology (TI-83 graphing calculators are highlighted) is incorporated throughout the text and the problems, as well as in the special group activities and projects. The book also contains labs that use real data and practices that lead students step by step through the problem solving process. At De Anza, along with hundreds of other colleges across the country, the college audience involves a large number of ESL students as well as students from many disciplines. The ESL students, as well as the non-ESL students, have been especially appreciative of this text. They find it extremely readable and understandable. Collaborative Statistics has been used in classes that range from 20 to 120 students, and in regular, honor, and distance learning classes.
This text comprises a three–volume series on Calculus. The ﬁrst part covers material taught in many “Calc ” courses: limits, derivaves, and the basics of integraon, found in Chapters through . The second text covers material oen taught in “Calc :” integraon and its applicaons, along with an introducon to sequences, series and Taylor Polynomials, found in Chapters through . The third text covers topics common in “Calc ” or “mulvariable calc:” parametric equaons, polar coordinates, vector–valued funcons, and funcons of more than one variable, found in Chapters through.
Early Algebra: Research into its Nature, its Learning, its Teaching
This survey of the state of the art on research in early algebra traces the evolution of a relatively new field of research and teaching practice. With its focus on the younger student, aged from about 6 years up to 12 years, this volume reveals the nature of the research that has been carried out in early algebra and how it has shaped the growth of the field. The survey, in presenting examples drawn from the steadily growing research base, highlights both the nature of algebraic thinking and the ways in which this thinking is being developed in the primary and early middle school student.
Carolyn Kieran --- JeongSuk Pang --- Deborah Schifter --- Swee Fong Ng
This book was created by combining two previous books on logic and critical thinking, both made available under a Creative Commons license, and then adding some material so that the coverage matched that of commonly used logic textbooks.
Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continued to inﬂuence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a wellestablished branch of mathematics that ﬁnds applications in every area of scholarly activity from music to physics, and in daily experience from weather prediction to predicting the risks of new medical treatments.
An openly licensed applied calculus textbook, covering derivatives, integrals, and an intro to multivariable calculus. This book is heavily remixed from Dale Hoffman's Contemporary Calculus textbook, and retains the same conceptual focus from that text. License: Creative Commons Attribution. This license is considered to be some to be the most open license since it is the least restrictive. It allows reuse, remixing, and distribution (including commercial), only requiring attribution. The content can be remixed into content of other license, but on the other hand it allows the remix to be put under a more restrictive license.
This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.
This is a book about statistical mechanics at the advanced undergraduate level. It assumes a background in classical mechanics through the concept of phase space, in quantum mechanics through the Pauli exclusion principle, and in mathematics through multivariate calculus. (Section 9.2 also assumes that you can can diagonalize a 2 x 2 matrix.)
Proofs and Concepts: The Fundamentals of Abstract Mathematics
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 high-school students), or for use as a very inexpensive supplement to undergraduate courses in any field of abstract mathematics.
Active Calculus is different from most existing calculus texts in at least the following ways: the text is free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the text is open source, and interested instructors can gain access to the original source files upon request; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature. License: Creative Commons Attribution Sharealike Noncommercial. This license is very open. It allows reuse, remixing, and distribution, but prohibits commercial use and requires any remixes use the same license as the original. This limits where the content can be remixed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license. The non-commercial clause can make getting printed copies of remixes challenging depending upon how strictly the authors interpret the clause.
Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; version 2.0 now contains WeBWorK exercises in each chapter, which are fully interactive in the HTML format and included in print in the PDF; the text is open source, and interested users can gain access to the original source files on GitHub; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; following the WeBWorK exercises in each section, there are several challenging problems that require students to connect key ideas and write to communicate their understanding. For more information, see the author's website and blog. License: Creative Commons Attribution Sharealike Noncommercial. This license is very open. It allows reuse, remixing, and distribution, but prohibits commercial use and requires any remixes use the same license as the original. This limits where the content can be remixed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license. The non-commercial clause can make getting printed copies of remixes challenging depending upon how strictly the authors interpret the clause.
In Active Calculus - Multivariable, we endeavor to actively engage students in learning the subject through an activity-driven approach in which the vast majority of the examples are completed by students. Where many texts present a general theory of calculus followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore. Following key activities or examples, the presentation normally includes some overall perspective and a brief synopsis of general trends or properties, followed by formal statements of rules or theorems. While we often offer plausibility arguments for such results, rarely do we include formal proofs. It is not the intent of this text for the instructor or author to demonstrate to students that the ideas of calculus are coherent and true, but rather for students to encounter these ideas in a supportive, leading manner that enables them to begin to understand for themselves why calculus is both coherent and true.
There are key differences between the way teaching and learning takes place in high schools and universities. Our goal is much more than just getting you to reproduce what was done in the classroom. Here are some key points to keep in mind: • The pace of this course will be faster than a high school class in precalculus. Above that, we aim for greater command of the material, especially the ability to extend what we have learned to new situations. • This course aims to help you build the stamina required to solve challenging and lengthy multi-step problems. • As a rule of thumb, this course should on average take 15 hours of effort per week. That means that in addition to the 5 classroom hours per week, you would spend 10 hours extra on the class. This is only an average and my experience has shown that 12–15 hours of study per week (outside class) is a more typical estimate. In other words, for many students, this course is the equivalent of a halftime job! • Because the course material is developed in a highly cumulative manner, we recommend that your study time be spread out evenly over the week, rather than in huge isolated blocks. An analogy with athletics is useful: If you are preparing to run a marathon, you must train daily; if you want to improve your time, you must continually push your comfort zone.
Precalculus: An Investigation of Functions (Includes Trig) 1st Ed
The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus. The second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisited more extensively in the third chapter. As with the first part of the book, an emphasis is placed on motivating the concepts and on modeling and interpretation. This book attempts to find a balance between a modern approach to precalculus focusing on applications, problem solving, and concepts and a traditional approach, emphasizing the basic skills needed for calculus. License: Creative Commons Attribution Sharealike. This license is considered to be some to be the most open license. It allows reuse, remixing, and distribution (including commercial), but requires any remixes use the same license as the original. This limits where the content can be remixed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license.
Precalculus: An Investigation of Functions (Includes Trig) 2nd Ed
The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus. The second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisited more extensively in the third chapter. As with the first part of the book, an emphasis is placed on motivating the concepts and on modeling and interpretation. This book attempts to find a balance between a modern approach to precalculus focusing on applications, problem solving, and concepts and a traditional approach, emphasizing the basic skills needed for calculus. The second edition adds sections on real and complex roots of polynomials, dot product, and a new chapter on conics. License: Creative Commons Attribution Sharealike. This license is considered to be some to be the most open license. It allows reuse, remixing, and distribution (including commercial), but requires any remixes use the same license as the original. This limits where the content can be remixed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license.
Math in Society is a free, open textbook. This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. This book is appropriate for Math 107 (Washington State Community Colleges common course number).
Precalculus An Investigation of Functions Edition 1.5
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.
Algebraic, Analytic, and Computational Number Theory and Its Applications
Analytic number theory is a branch of number theory which uses methods from mathematical analysis in order to solve difficult problems about integers. Analytic number theory can be split into two major areas: multiplicative number theory and additive number theory.
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
Neutrosophic Multi-Criteria Decision Making
Neutrosophic logic and set are gaining significant attention in solving many real-life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. A number of new neutrosophic theories have been proposed and have been applied in Multi-Criteria Decision-Making, computational intelligence, multiple-attribute decision-making, image processing, medical diagnosis, fault diagnosis, optimization design, and so on. Neutrosophic logic, set, probability, statistics, etc., are, respectively, generalizations of fuzzy and intuitionistic fuzzy logic and set, classical and imprecise probability, classical statistics and so on.
Florentin Smarandache (Ed.) --- Jun Ye (Ed.) --- Yanhui Guo (Ed.)
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.
A Spiral Workbook for Discrete Mathematics
This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students’ problem-solving and writing skills.
Introduction to the Modeling and Analysis of Complex Systems
Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example.
Calculus For the Life Sciences: A Modeling Approach Volume I
In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There is a chapter on systems of two difference equations.
Calculus for The Life Sciences A Modeling Approach Volume II
Welcome to Early Childhood Mathematics! This course satisfies the Early Childhood Unified requirements in the state of Kansas for a teaching license Birth to Grade 3. Most people agree that early childhood includes the period from infancy until eight years of age, characterized by rapid and complex growth in physical, cognitive, and social domains. Math skills must be taught in early childhood. Children should be provided a foundation to succeed in elementary school and beyond. Teachers should focus lessons in early childhood around the basic skills that will help to advance future mathematics. From preschool to the end of elementary school, children are setting the foundation for future life skills.
The text is mostly an adaptation of two other excellent open- source calculus textbooks: Active Calculus by Dr. Matt Boelkins of Grand Valley State University and Drs. Gregory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar, and Jennifer Bowen of the Virginia Military Institute and Mount Saint Mary's University. Both of these texts can be found at http://aimath.org/textbooks/approved-textbooks/. The authors of this text have combined sections, examples, and exercises from the above two texts along with some of their own content to generate this text. The impetus for the creation of this text was to adopt an open-source textbook for Calculus while maintaining the typical schedule and content of the calculus sequence at our home institution.
This text for Analytic Geometry and Calculus I, II, and III is a Dalton State College remix of APEX Calculus 3.0. The text was created through a Round Six ALG Textbook Transformation Grant. Topics covered in this text include: Limits Derivatives Integration Antidifferentiation Sequences Vectors
The Simple Math of Writing Well: Writing for the 21st Century
Writing guides abound, but The Simple Math of Writing Well is one of a kind. Readers will find its practical approach affirming, encouraging, and informative, and its focus on the basics of linguistic structure releases 21st-century writers to embrace the variety of mediums that define our internet-connected world. As Harrop reminds us in the opening chapters of her book, we write more today than ever before in history: texts, emails, letters, blogs, reports, social media posts, proposals, etc. The Simple Math of Writing Well is the first guide that directly addresses the importance of writing well in the Google age.
Combinatorics is a subfield of "discrete mathematics," so we should begin by asking what discrete mathematics means. The differences are to some extent a matter of opinion, and various mathematicians might classify specific topics differently. "Discrete" should not be confused with "discreet," which is a much more commonly-used word. They share the same Latin root, "discretio," which has to do with wise discernment or separation. In the mathematical "discrete," the emphasis is on separateness, so "discrete" is the opposite of \continuous." If we are studying objects that can be separated and treated as a (generally countable) collection of units rather than a continuous structure, then this study falls into discrete mathematics. In calculus, we deal with continuous functions, so calculus is not discrete mathematics. In linear algebra, our matrices often have real entries, so linear algebra also does not fall into discrete mathematics.Text books on discrete mathematics often include some logic, as discrete mathematics is often used as a gateway course for upper-level math. Elementary number theory and set theory are also sometimes covered. Algorithms are a common topic, as algorithmic techniques tend to work very well on the sorts of structures that we study in discrete mathematics. In Combinatorics, we focus on combinations and arrangements of discrete structures. There are have major branches of combinatorics that we will touch on in this course: enumeration, graph theory, Ramsey Theory, design theory, and coding theory. (The related topic of cryptography can also be studied in combinatorics, but we will not touch on it in this course.) We will focus on enumeration, graph theory, and design theory, but will briey introduce the other two topics.
Introduction to Modern Set Theory is designed for a one-semester course in set theory at the advanced undergraduate or beginning graduate level. Three features are the full integration into the text of the study of models of set theory, the use of illustrative examples both in the text and in the exercises, and the integration of consistency results and large cardinals into the text early on. This book is aimed at two audiences: students who are interested in studying set theory for its own sake, and students in other areas who may be curious about applications of set theory to their field. In particular, great care is taken to develop the intuitions that lie behind modern, as well as classical, set theory, and to connect set theory with the rest of mathematics.
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 consist 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. Above all, this book is dedicated to the principle that doing mathematics is fun. As long as you know that some of the problems are going to require more than one attempt before you hit on the main idea, you can relax and enjoy your successes, knowing that as you work more and more problems and share more and more ideas, problems that seemed intractable at first become a source of satisfaction later on. There are six chapters as well as an appendix with three additional topics: What is Combinatorics? Applications of Induction and Recursion in Combinatorics and Graphy Theory Distribution Problems Generating Functions The Principle of Inclusion and Exclusion Groups Acting on Sets The three supplmental sections deal with relations, mathematical induction, and exponential generating functions.
Advanced Algebra II: Conceptual Explanations
This module contains a table of every module within the three books of Kenny Felder's course on "Algebra II", with links to the modules.
By definition scientists are an inquisitive lot. But what are the scientific curiosities and concerns on the minds of Australians? What worries them, baffles them, and sets their curiosity meter to 10 out of 10? To find out, the Office of the Chief Scientist (OCS) took the nation’s intellectual temperature, surveying 1186 Australians: men and women aged 18 to 65, from all education levels and locations around Australia. The results frame this book: a collection of essays covering the diverse areas of science Australians are curious about. Edited by eminent science writer Leigh Dayton and including a foreword from Australia’s Chief Scientist, Ian Chubb. The collection covers a range of issues, including food and farming technology, environmental upheaval, health, fuel and energy technology and space exploration.
The author invites the reader to embark on a journey through the interesting and surprising subject of sequences and series of real numbers and functions in this clear and easy-to-read theoretical exposition. The book provides several examples and applications of sequences and series, as well as a list of proposed exercises to provide a full learning experience. From the secondary to the university level, this textbook provides a solid foundation in mathematics and a basis for further studies.
Introduction to Logic and Critical Thinking Version 1.4
Introduction to Logic and Critical Thinking
This is an introductory textbook in logic and critical thinking. The goal of the textbook is to provide the reader with a set of tools and skills that will enable them to identify and evaluate arguments. The book is intended for an introductory course that covers both formal and informal logic. As such, it is not a formal logic textbook, but is closer to what one would find marketed as a “critical thinking textbook.” The formal logic in chapter 2 is intended to give an elementary introduction to formal logic. Specifically, chapter 2 introduces several different formal methods for determining whether an argument is valid or invalid (truth tables, proofs, Venn diagrams). I contrast these formal methods with the informal method of determining validity introduced in chapter 1. What I take to be the central theoretical lesson with respect to the formal logic is simply that of understanding the difference between formal and informal methods of evaluating an argument’s validity. I believe there are also practical benefits of learning the formal logic. First and foremost, once one has internalized some of the valid forms of argument, it is easy to impose these structures on arguments one encounters. The ability to do this can be of use in evaluating an argumentative passage, especially when the argument concerns a topic with which one is not very familiar (such as on the GRE or LSAT).
There’s an ancient view, still widely held, that what makes human beings special—what distinguishes us from the “beasts of the field”—is that we are rational. What does rationality consist in? That’s a vexed question, but one possible response goes roughly like this: we manifest our rationality by engaging in activities that involve reasoning—making claims and backing them up with reasons, acting in accord with reasons and beliefs, drawing inferences from available evidence, and so on. This reasoning activity can be done well and it can be done badly—it can be done correctly or incorrectly. Logic is the discipline that aims to distinguish good reasoning from bad. Since reasoning is central to all fields of study—indeed, since it’s arguably central to being human—the tools developed in logic are universally applicable. Anyone can benefit from studying logic by becoming a more self-aware, skillful reasoner. This covers a variety of topics at an introductory level. Chapter One introduces basic notions, such as arguments and explanations, validity and soundness, deductive and inductive reasoning; it also covers basic analytical techniques, such as distinguishing premises from conclusions and diagramming arguments. Chapter Two discusses informal logical fallacies. Chapters Three and Four concern deductive logic, introducing the basics of Aristotelian and Sentential Logic, respectively. Chapters Five and Six concern inductive logic. Chapter Five deals with analogical and causal reasoning, including a discussion of Mill’s Methods. Chapter Six covers basic probability calculations, Bayesian inference, fundamental statistical concepts and techniques, and common statistical fallacies.
This book covers calculus in two and three variables. It is suitable for a one-semester course, normally known as “Vector Calculus”, “Multivariable Calculus”, or simply “Calculus III”. The prerequisites are the standard courses in single-variable calculus (a.k.a. Calculus I and II). I have tried to be somewhat rigorous about proving results. But while it is important for students to see full-blown proofs - since that is how mathematics works - too much rigor and emphasis on proofs can impede the ﬂow of learning for the vast majority of the audience at this level. If I were to rate the level of rigor in the book on a scale of 1 to 10, with 1 being completely informal and 10 being completely rigorous, I would rate it as a 5.
As we hope you will sense right from the beginning, we believe that combinatorial mathematics is one of the most fascinating and captivating subjects on the planet. Combinatorics is very concrete and has a wide range of applications, but it also has an intellectually appealing theoretical side. Our goal is to give you a taste of both. In order to begin, we want to develop, through a series of examples, a feeling for what types of problems combinatorics addresses.
Emerging Technologies towards Energy Cooperation between Smart Grid and Microgrids
The growing propagation of microgrids and their remarkable effects on the operation of the smart grid is leading to the development of a sustained environment which is moving away from traditional frameworks. Therefore, tending to microgrid systems to increase their range of benefits can play a significant role in outlining an effective negotiation framework for the microgrids that are connected to the smart grid.
lgebraic principles. The text is suitable for a typical introductory Algebra & Trigonometry course, and was developed to be used flexibly. The modular approach and the richness of content ensures that the book meets the needs of a variety of programs. Algebra and Trigonometry guides and supports students with differing levels of preparation and experience with mathematics. Ideas are presented as clearly as possible, and progress to more complex understandings with considerable reinforcement along the way. A wealth of examples – usually several dozen per chapter – offer detailed, conceptual explanations, in order to build in students a strong, cumulative foundation in the material before asking them to apply what they’ve learned.
his text was written to be used as the primary text for the class Discrete Mathematics (Math 228) at the University of Northern Colorado. The course serves as the role of a transitions course (introduction to proof), as well as an introduction to topics in discrete mathematics. While we have a few students each semester who will go on to study computer science, pure mathematics or applied mathematics, the majority of students are studying to be elementary or secondary math teachers. For this reason, most of the standard discrete textbooks are not appropriate for us. For many years we used Discrete and Combinatorial Mathematics by Richard Grassl and Tabitha Mingus. This is a very nice book in many ways (Grassl taught at UNC) but the print-on-demand publishing was expensive for students and some sections needed updating and (as I saw it) rearranging. While the book began as a set of lecture notes, it now contains a number of features that should support its use as a primary textbook: 363 exercises, including 233 with answers or full solutions, as well as 130 more involved problems suitable for homework. Investigate! activities throughout the text to support active, inquiry based learning. A full index and list of symbols. Consistent and (hopefully) helpful page layout and formatting (i.e., examples are easy to identify, important definitions and theorems in boxes, etc.)
Mathematical Reasoning: Writing and Proof
Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs. Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout. For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills
This module develops concepts and techniques for studying functions. You will learn about one of the foundations of applied mathematics, i.e. the algebraic and graphic methods for studying functions. You'll be introduced to clear define and recognize functions, see how they constitute a special type of relation, and then move on to consider the simple, useful class of functions called linear functions. Along the way you'll have plenty of chances to practise what you're learning in examples and exercises.
Everyone in Hong Kong has heard of the Mark Six! Players select six different numbers from 49 possibilities in the hope of winning a small fortune - or possibly even a large one. So how many different choices of six numbers out of 49 are there? If you just sat down to count out all the possible combination, it would take you a very long time indeed. But in mathematics we have other counting tools that can assist us in this counting task. Learning to use these tools is the basis for learning about counting and probability. The first section in this module introduces basic counting principles, and helps you work through some simple counting problems. You will learn how the Addition and Multiplication Principles can be applied to determine the number of possible combinations. You will then look at two important counting tools, namely permutations and combinations, and compare the different counting principle between them. The second section in this module introduces you to probability as a measure of chance. It gives you a numerical means of comparing different degrees of chance. You learn by looking at common games of chance: tossing a coin, selecting a playing card, or throwing dice.
This textbook, or really a “coursebook” for a college freshman-level class, has been updated for Spring 2014 and provides an introduction to programming and problem solving using both Matlab and Mathcad. We provide a balanced selection of introductory exercises and real-world problems (i.e. no “contrived” problems). We include many examples and screenshots to guide the reader. We assume no prior knowledge of Matlab or Mathcad.
Elementary Differential Equations with Boundary Value Problems
Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. 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 1695 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 definitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 250 completely worked out examples. Where appropriate, concepts and results are depicted in 144 figures. Although I believe that the computer is an immensely valuable tool for learning, doing, and writing mathematics, the selection and treatment of topics in this text reflects my pedagogical orientation along traditional lines. However, I have incorporated what I believe to be the best use of modern technology, so you can select the level of technology that you want to include in your course. The text includes 336 exercises – identified by the symbols C and C/G – that call for graphics or computation and graphics. There are also 73 laboratory exercises – identified by L – that require extensive use of technology. In addition, several sections include informal advice on the use of technology. If you prefer not to emphasize technology, simply ignore these exercises and the advice.
Part of the NCSSM Online AP Calculus Collection: This video deals with transformations of functions including parent functions and the library of functions and relations. http://www.dlt.ncssm.edu Please attribute this work as being created by the North Carolina School of Science and Mathematics. This work is licensed under Creative Commons CC-BY http://creativecommons.org/licenses/by/3.0 Help us caption & translate this video! http://amara.org/v/GAfN/
NCSSMDistanceEd published via YouTube.com
Creative Commons License
What is PURE MATHEMATICS? What does PURE MATHEMATICS mean? PURE MATHEMATICS meaning - PURE MATHEMATICS definition - PURE MATHEMATICS explanation. Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license. Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts. This was a recognizable category of mathematical activity from the nineteenth century onwards, at variance with the trend towards meeting the needs of navigation, astronomy, physics, economics, engineering, and so on. Another insightful view put forth is that pure mathematics is not necessarily applied mathematics: it is possible to study abstract entities with respect to their intrinsic nature, and not be concerned with how they manifest in the real world. Even though the pure and applied viewpoints are distinct philosophical positions, in practice there is much overlap in the activity of pure and applied mathematicians. To develop accurate models for describing the real world, many applied mathematicians draw on tools and techniques that are often considered to be "pure" mathematics. On the other hand, many pure mathematicians draw on natural and social phenomena as inspiration for their abstract research. Input by Sofia Nelly
The Audiopedia published via YouTube.com
Creative Commons License This video represents licensed content on YouTube, meaning that the content has been claimed by a YouTube content partner.
There are some key angles that have exact values in trigonometry. The ones we need to know are 0, 30, 45, 60 and 90. In this video we will discover one method of remember what these values are - by counting fingers on our hand! In the first part we discovered a different method (constructing a table) which you may prefer. Choose whichever method works best for you. SUBSCRIBE to the FuseSchool YouTube channel for many more educational videos. Our teachers and animators come together to make fun & easy-to-understand videos in Chemistry, Biology, Physics, Maths & ICT. VISIT us at www.fuseschool.org, where all of our videos are carefully organised into topics and specific orders, and to see what else we have on offer. Comment, like and share with other learners. You can both ask and answer questions, and teachers will get back to you. These videos can be used in a flipped classroom model or as a revision aid. Find all of our Chemistry videos here: https://www.youtube.com/watch?v=cRnpKjHpFyg&list=PLW0gavSzhMlReKGMVfUt6YuNQsO0bqSMV Find all of our Biology videos here: https://www.youtube.com/watch?v=tjkHzEVcyrE&list=PLW0gavSzhMlQYSpKryVcEr3ERup5SxHl0 Find all of our Maths videos here: https://www.youtube.com/watch?v=hJq_cdz_L00&list=PLW0gavSzhMlTyWKCgW1616v3fIywogoZQ Twitter: https://twitter.com/fuseSchool Access a deeper Learning Experience in the FuseSchool platform and app: www.fuseschool.org Follow us: http://www.youtube.com/fuseschool Friend us: http://www.facebook.com/fuseschool This Open Educational Resource is free of charge, under a Creative Commons License: Attribution-NonCommercial CC BY-NC ( View License Deed: http://creativecommons.org/licenses/by-nc/4.0/ ). You are allowed to download the video for nonprofit, educational use. If you would like to modify the video, please contact us: info@fuseschool.org Input by Sofia Nelly
FuseSchool - Global Education published via YouTube.com
A description of the concepts behind Analysis of Variance. Also, see this site: http://www.psych.utah.edu/stat/introstats/anovaflash.html for a "hands-on" experience.
J David Eisenberg published via YouTube.com
Applied Finite Mathematics covers topics including linear equations, matrices, linear programming, the mathematics of finance, sets and counting, probability, Markov chains, and game theory.
All of mathematics summarised in one poster.