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e-book
This version of YAINTT has a particular emphasis on connections to cryptology. The cryptologic material appears in Chapter 4 and §§5.5 and 5.6, arising naturally (I hope) out of the ambient number theory. The main cryptologic applications – being the RSA cryptosystem, Diffie-Hellman key exchange, and the ElGamal cryptosystem – come out so naturally from considerations of Euler’s Theorem, primitive roots, and indices that it renders quite ironic G.H. Hardy’s assertion [Har05] of the purity and eternal inapplicability of number theory. Note, however, that once we broach the subject of these cryptologic algorithms, we take the time to make careful definitions for many cryptological concepts and to develop some related ideas of cryptology which have much more tenuous connections to the topic of number theory. This material therefore has something of a different flavor from the rest of the text – as is true of all scholarly work in cryptology (indeed, perhaps in all of computer science), which is clearly a discipline with a different culture from that of “pure”mathematics. Obviously, these sections could be skipped by an uninterested reader, or remixed away by an instructor for her own particular class approach.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Number theory Textbooks
- Resource Type:
- e-book
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e-book
I intend this book to be, firstly, a introduction to calculus based on the hyperrealnumber system. In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, I will provide none for the hyperreals. The reader interested in questions of foundations should consult books such asAbraham Robinson's Non-standard Analysis or Robert Goldblatt's Lectures onthe Hyperreals. Secondly, I have aimed the text primarily at readers who already have somefamiliarity with calculus. Although the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry, in practice the pace istoo fast for most of those without some acquaintance with the basic notions of calculus.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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e-book
An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Late transcendentals and multivariable versions are also available. This textbook has been used in classes at:Boise State University,Claremont McKenna College,University of Minnesota, University of Puget Sound, Western Connecticut State University, Whitman College.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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e-book
This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them. So this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read but rather to be engaged. Since this can be a difficult task, there are several features of the book designed to assist students in this endeavor. In particular, most sections of the book start with a beginning activity that review prior mathematical work that is necessary for the new section or introduce new concepts and definitions that will be used later in that section. Each section also contains several progress checks that are short exercises or activities designed to help readers determine if they are understanding the material. In addition, the text contains links to several interactive Geogebra applets or worksheets. These applets are usually part of a beginning activity or a progress check and are intended to be used as part of the textbook.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Textbooks
- Resource Type:
- e-book
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e-book
The precursors to what we study today as Trigonometry had their origin in ancient Mesopotamia, Greece and India. These cultures used the concepts of angles and lengths as an aid to understanding the movements of the heavenly bodies in the night sky. Ancient trigonometry typically used angles and triangles that were embedded in circles so that many of the calculations used were based on the lengths of chords within a circle. The relationships between the lengths of the chords and other lines drawn within a circle and the measure of the corresponding central angle represent the foundation of trigonometry - the relationship between angles and distances.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Textbooks
- Resource Type:
- e-book
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e-book
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 self-study. 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:
- e-book
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e-book
"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 entry-level trades training resource, while still offering the flexibility for lines to be used as stand-alone books"--BC Campus website.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks Geometry
- Resource Type:
- e-book
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e-book
Think Stats is an introduction to Probability and Statistics for Python programmers. Think Stats emphasizes simple techniques you can use to explore real data sets and answer interesting questions. The book presents a case study using data from the National Institutes of Health. Readers are encouraged to work on a project with real datasets. If you have basic skills in Python, you can use them to learn concepts in probability and statistics. Think Stats is based on a Python library for probability distributions (PMFs and CDFs). Many of the exercises use short programs to run experiments and help readers develop understanding.
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Textbooks Statistics -- Computer programs
- Resource Type:
- e-book
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e-book
Think Bayes is an introduction to Bayesian statistics using computational methods. The premise of this book, and the other books in the Think X series, is that if you know how to program, you can use that skill to learn other topics. Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. This book uses Python code instead of math, and discrete approximations instead of continuous mathematics. As a result, what would be an integral in a math book becomes a summation, and most operations on probability distributions are simple loops. I think this presentation is easier to understand, at least for people with programming skills. It is also more general, because when we make modeling decisions, we can choose the most appropriate model without worrying too much about whether the model lends itself to conventional analysis. Also, it provides a smooth development path from simple examples to real-world problems.
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Bayesian statistical decision theory Python (Computer program language) Textbooks
- Resource Type:
- e-book
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e-book
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 "game-based" 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:
- e-book
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e-book
It is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside. The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline. The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks
- Resource Type:
- e-book
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e-book
This textbook was born of a desire to contribute a viable, free, introductory Numerical Analysis textbook for instructors and students of mathematics. The ultimate goal of Tea Time Numerical Analysis is to be a complete, one-semester, single-pdf, downloadable textbook designed for mathematics classes. Now includes differential equations. Over 350 pages Over 1000 lines of code Over 200 figures Open source
- Subjects:
- Mathematics and Statistics
- Keywords:
- Numerical analysis -- Data processing Textbooks
- Resource Type:
- e-book
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e-book
"This book is a polished version of the author's notes for a course entitled Several Complex Variables. It should be suitable for a semester-long topics course or for self-study 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 semester-long 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:
- e-book
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e-book
This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. It is targeted to the typical Statistics 101 college student, and covers the topics typically covered in the first semester of such a course. It is freely available under the Creative Commons License, and includes a software library in Python for making some of the calculations and visualizations easier.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical statistics Textbooks
- Resource Type:
- e-book
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e-book
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.Open SUNY Textbooks is an open access textbook publishing initiative established by State University of New York libraries and supported by SUNY Innovative Instruction Technology Grants. This initiative publishes high-quality, cost-effective course resources by engaging faculty as authors and peer-reviewers, and libraries as publishing service and infrastructure. The pilot launched in 2012, providing an editorial framework and service to authors, students and faculty, and establishing a community of practice among libraries. Participating libraries in the 2012- 2013 pilot include SUNY Geneseo, College at Brockport, College of Environmental Science and Forestry, SUNY Fredonia, Upstate Medical University, and University at Buffalo, with support from other SUNY libraries and SUNY Press. More information can be found at http://textbooks.opensuny.org.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks Computer science -- Mathematics
- Resource Type:
- e-book
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e-book
This text is intended to support courses that bridge the divide between mathematics typically encountered in U.S. high school curricula and the practical problems that natural resource students might engage with in their disciplinary coursework and professional internships.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Problem solving Applied mathematics Textbooks Numerical analysis
- Resource Type:
- e-book
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e-book
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.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks
- Resource Type:
- e-book
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e-book
You are probably asking yourself the question, "When and where will I use statistics?". If you read any newspaper or watch television, or use the Internet, you will see statistical information. There are statistics about crime, sports, education, politics, and real estate. Typically, when you read a newspaper article or watch a news program on television, you are given sample information. With this information, you may make a decision about the correctness of a statement, claim, or "fact." Statistical methods can help you make the "best educated guess."
- Subjects:
- Management and Mathematics and Statistics
- Keywords:
- Industrial management -- Statistical methods Commercial statistics Textbooks
- Resource Type:
- e-book
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e-book
Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry. 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. In addition to the paper homework sets, algorithmetically generated online homework is available as part of a complete course shell package, which also includes a sample syllabus, teacher notes with lecture examples, sample quizzes and exams, printable classwork sheets and handouts, and chapter review problems. If you teach in Washington State, you can find the course shell in the WAMAP.org template course list. For those located elsewhere, you can access the course shell at MyOpenMath.com. A self-study version of the online course exercises is also available on MyOpenMath.com for students wanting to learn the material on their own, or who need a refresher.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Algebra Textbooks
- Resource Type:
- e-book
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e-book
A casual glance through the Table of Contents of most of the major publishers' College Algebra books reveals nearly isomorphic content in both order and depth. Our Table of Contents shows a different approach, one that might be labeled “Functions First.” To truly use The Rule of Four, that is, in order to discuss each new concept algebraically, graphically, numerically and verbally, it seems completely obvious to us that one would need to introduce functions first. (Take a moment and compare our ordering to the classic “equations first, then the Cartesian Plane and THEN functions” approach seen in most of the major players.) We then introduce a class of functions and discuss the equations, inequalities (with a heavy emphasis on sign diagrams) and applications which involve functions in that class. The material is presented at a level that definitely prepares a student for Calculus while giving them relevant Mathematics which can be used in other classes as well. Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The answers to nearly all of the computational homework exercises are given in thetext and we have gone to great lengths to write some very thought provoking discussion questions whose answers are not given. One will notice that our exercise sets are much shorter than the traditional sets of nearly 100 “drill and kill” questions which build skill devoid of understanding. Our experience has been that students can do about 15-20 homework exercises a night so we very carefully chose smaller sets of questions which cover all of the necessary skills and get the students thinking more deeply about the Mathematics involved.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Algebra Textbooks
- Resource Type:
- e-book