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Precalculus
Thomas Tradler; Holly Carley · CUNY Academic Works · 2015
These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems. This course in precalculus has the overarching theme of “functions.” This means that many of the often more algebraic topics studied in the previous courses are revisited under this new function theoretic point of view. However, in order to keep this text as self contained as possible we always recall all results that are necessary to follow the core of the course even if we assume that the student has familiarity with the formula or topic at hand. After a first introduction to the abstract notion of a function, we study polynomials, rational functions, exponential functions, logarithmic functions, and trigonometric functions with the function viewpoint. Throughout, we will always place particular importance to the corresponding graph of the discussed function which will be analyzed with the help of the TI-84 calculator as mentioned above. These are in fact the topics of the first four (of the five) parts of this precalculus course. In the fifth and last part of the book, we deviate from the above theme and collect more algebraically oriented topics that will be needed in calculus or other advanced mathematics courses or even other science courses. This part includes a
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Introduction to Mathematical Analysis I
Beatriz Lafferriere; Gerardo Lafferriere; Mau Nam Nguyen · Portland State University Library · 2016
Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs. The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds. The second edition includes a number of improvements based on recommendations from students and colleagues and on our own experience teaching the course over the last several years. In this edition we streamlined the narrative in several sections, added more proofs, many examples worked out in detail, and numerous new exercises. In all we added over 50 examples in the main text and 100 exercises (counting parts).
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A Computational Introduction to Number Theory and Algebra
Victor Shoup · Cambridge University Press · 2009
All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well. The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures. There are a few sections that are marked with a “(∗),” indicating that the material covered in that section is a bit technical, and is not needed else- where. There are many examples in the text, which form an integral part of the book, and should not be skipped. There are a number of exercises in the text that serve to reinforce, as well as to develop important applications and generali
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Combinatorics Through Guided Discovery
Kenneth Bogart · Kenneth P. Bogart · 2004
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 metho
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Introduction to Real Analysis
William Trench · A.T. Still University · 2013
This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.
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Math in Society
David Lippman · David Lippman · 2017
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).
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Basic Analysis: Introduction to Real Analysis
Jirí Lebl · Jirí Lebl · 2016
This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces.
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OpenIntro Statistics
David Diez; Christopher Barr; Mine Cetinkaya-Rundel · OpenIntro · 2019
OpenIntro Statistics covers a first course in statistics, providing a rigorous introduction to appliedstatistics that is clear, concise, and accessible. This book was written with the undergraduate levelin mind, but it’s also popular in high schools and graduate courses.We hope readers will take away three ideas from this book in addition to forming a foundationof statistical thinking and methods. • Statistics is an applied field with a wide range of practical applications.• You don’t have to be a math guru to learn from real, interesting data.• Data are messy, and statistical tools are imperfect. But, when you understand the strengthsand weaknesses of these tools, you can use them to learn about the world.
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Precalculus
Carl Stitz; Jeff Zeager · Stitz Zeager Open Source Mathematics · 2013
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.
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Elementary Algebra
John Redden · Saylor Foundation · 2011
It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, elementary algebra and intermediate algebra. This textbook, Elementary Algebra, is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course. This text is, by far, the best elementary algebra textbook offered under a Creative Commons license. It is written in such a way as to maintain maximum flexibility and usability. A modular format was carefully integrated into the design. For example, certain topics, like functions, can be covered or omitted without compromising the overall flow of the text. An introduction of square roots in Chapter 1 is another example that allows for instructors wishing to include the quadratic formula early to do so. Topics such as these are carefully included to enhance the flexibility throughout. This textbook will effectively enable traditional or nontraditional approaches to elementary algebra. This, in addition to robust and diverse exercise sets, provides the base for an excellent individualized textbook instructors can use free of needless edition changes and excessive costs! A few other differences are highlighted below: Equivalent mathematical notation using standard text found on a keyboard A variety of applications and word problems included in most exercise sets Clearly enumerated steps found in context within carefully chosen examples Alternative methods and notation, modularly integrated, where appropriate Video examples available, in context, within the online version of the textbook Robust and diverse exercise sets with di
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Tort Law: Cases and Commentaries
Samuel Beswick · CanLII: Canadian Legal Information Institute · 2021
The law of obligations concerns the legal rights and duties owed between people. Three primary categories make up the common law of obligations: tort, contract, and unjust enrichment. This casebook provides an introduction to tort law: the law that recognises and responds to civil wrongdoing. The material is arranged in two parts. Part I comprises §§1-11 and addresses intentional and dignitary torts and the overarching theories and goals of tort law. Part II comprises §§12-25 and addresses no-fault compensation schemes, negligence, nuisance, strict liability, and tort law’s place within our broader legal systems. This casebook was compiled and edited by Assistant Professor Samuel Beswick of the University of British Columbia Peter A. Allard School of Law. Maddison Zapach (J.D. expected 2023) provided research assistance on the first edition (published July 2021). We gratefully acknowledge the influence on our approach to this subject of Professor Joost Blom QC of the Allard School of Law, Professor John C.P. Goldberg of Harvard Law School, and Associate Professor Rosemary Tobin of the University of Auckland Faculty of Law. The support of Open UBC and the UBC Teaching and Learning Enhancement Fund is also gratefully acknowledged.
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Antitrust: Principles, Cases, and Materials
Daniel Francis; Christopher Sprigman · Daniel Francis and Christopher Jon Sprigman · 2026
Antitrust: Principles, Cases, and Materials (4th Edition) is a free antitrust law textbook designed for a three-credit or four-credit antitrust course (we teach the four-credit course at NYU School of Law).
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Mental Disorders and the Criminal Justice System
Anne Nichol; Kendra Harding; Monica McKirdy · Open Oregon Educational Resources · 2025
This is an introductory textbook exploring the management and treatment of people with mental disorders throughout the criminal justice system.
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Rules and Laws for Civil Actions
Stella Elias; Derek Muller; Jason Rantanen · University of Iowa · 2022
Rules and Laws for Civil Actions is an open-access resource for law students containing the U.S. Constitution, Federal Rules of Civil Procedure, Federal Rules of Evidence, Federal Rules of Appellate Procedure, and selected federal and state statutes. The book was created by a team of faculty members at the University of Iowa College of Law to supplement the study of Civil Procedure, Evidence, Constitutional Law, and other law school courses. In addition to containing the official text, each legal source found in Rules and Laws for Civil Actions is accompanied by an introductory section written by an Iowa Law professor explaining its significance and background.
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Transactional Drafting: Introduction to Contract Drafting and Transactional Practice
Ben Fernandez · Ben Fernandez · 2021
Transactional Drafting: Introduction to Contract Drafting and Transactional Practice contains a condensed presentation of all of the topics typically covered in an upper-level law school class on contract drafting. The book covers drafting from scratch including writing in plain English (not using legalese), avoiding ambiguity, and drafting covenants, rights and prohibitions consistently (using "will" or "shall" for covenants, "may" for rights, and "will not" or "shall not" for prohibitions). And it covers contract organization, from the title and the exordium to the core covenant, deal provisions and "boilerplate," to the testimonium and the signature blocks. The book also includes material on getting up to speed before you start drafting and brainstorming for contingencies after you have finished. In addition to drafting from scratch the book introduces students to the wide range of skills involved in transactional practice. There are chapters on revising form documents, both when you are the original drafter and when you represent the other side. Also, the book includes chapters on negotiating contract language, handling a closing (i.e., verifying authority and getting the documents signed), dealing with ethical issues that arise in contract drafting and execution, drafting a contract amendment, and using computers to draft contracts. Transactional Drafting includes everything students need to know to “hit the ground running” as a transactional attorney.
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Legal Writing I & II: Legal Research and Writing & Introduction to Litigation Practice
Ben Fernandez · Ben Fernandez · 2020
Legal Writing I & II; Legal Research and Writing & Introduction to Litigation Practice contains a brief discussion of all of the topics covered in a law school courses on legal writing, including a typical first semester course on legal research, analysis and writing an objective memorandum, as well as a second semester course on persuasion and writing an appellate brief, motion to dismiss or motion for summary judgment. The discussion focuses on the basics of analogical reasoning and persuasion and leaves out the minutiae. Each topic is taken one step at a time, with each step building on the step before it. The sources of law are presented first, then legal research, and reading and analyzing cases and statutes. The book covers analogizing a case to a fact pattern and marshaling the relevant facts to the elements of a statutory rule next. And then first section of the book concludes with legal citation, CRAC and CREAC, and writing a legal research memorandum. The text also includes a lot of samples and examples of how the author would write a case brief, a legal memoranda and an appellate brief, as well as an appendix with charts, outlines and exercises students can use to practice these skills. Legal Writing I & II; Legal Research and Writing & Introduction to Litigation Practice covers all the skills students need to know to work at a law firm, and everything students have to learn to begin practicing in litigation department of a firm.
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Religion in the Law: An Open Access Casebook
Joe Dunman · L. Joe Dunman · 2026
This casebook features over 70 cases from American courts that involve, in some important way, religious belief and action. The book is divided into sections: First Principles, Establishment, Free Exercise, and Special Problems. Each section includes landmark or otherwise influential cases that have influenced American law and religious practice. Most cases come from the U.S. Supreme Court but the lower federal and state courts are also represented.In the contextual introductions to each section and subpart, I have tried to give the reader a basis for understanding how the cases came about and why I chose them for this book. I have tried to minimize editorial comment. I have cited some scholarship where I think it would be helpful, but please do not mistake this as an attempt to produce a comprehensive treatise on the subject of religion in the law. It is a casebook, and a short one, all things considered. At the end of each introductory part is a short “further reading” list. I chose those articles because I found each of them interesting and useful to understanding the topics that precede them. Their selection is not necessarily an endorsement of each author’s arguments, though I do agree with some of them.I designed this casebook specifically for my own use upper level law school seminar called Law & Religion. Class sessions using this book are intended to be student-led, round table talks with the professor acting as discussion prompter and neutral mediator. Generally, 2-5 cases are assigned for each class session. I selected, edited, and arranged the cases to complement each other thematically and chronologically to the best of my ability. Many of the cases include overlapping topics and could fit into multiple categories, so I took some liberties in their arrangement. Your mileage may vary.
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The Indigo Book: A Manual of Legal Citation
Christopher Sprigman · Public Resource · 2016
Welcome to The Indigo Book 2.0—a free, Creative Commons-dedicated implementation of the uniform system of citation commonly used in United States legal documents. The Indigo Book (2d ed. 2021) isn’t the same as The Bluebook: A Uniform System of Citation (21st ed. 2020), but it does implement the same system of citation that The Bluebook does. The scope of The Indigo Book’s coverage is roughly equivalent to The Bluebook’s “Bluepages”—that is, The Indigo Book covers legal citation for U.S. legal materials, as well as books, periodicals, and Internet and other electronic resources. For the materials that it covers, anyone using The Indigo Book will produce briefs, memoranda, law review articles, and other legal documents with citations that are compatible with the Uniform System of Citation. Although law students, scholars, and legal professionals sometimes talk about legal citation as if it is truly uniform, the fact is that legal citation has never actually been a uniform national system. Accordingly, The Indigo Book also provides insight into some of the discretionary preferences and jurisdiction specific variations found in legal citation throughout the United States.
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Global Corruption: Its Regulation under International Conventions, US, UK, and Canadian Law and Practice
Gerry Ferguson · University of Victoria · 2022
This book has been specifically created to make it easier for professors to offer a law school course on global corruption. It is also designed as a resource tool for all persons working in the anti-corruption field. The book is issued under a creative commons license and can be used for free in whole or in part for non-commercial purposes. The first chapter sets out the general context of global corruption: its nature and extent, and some views on its historical, social, economic and political dimensions. Each subsequent chapter sets out international standards and requirements in respect to combatting corruption – mainly in the UN Convention Against Corruption (UNCAC) and the OECD Bribery of Foreign Officials Convention (OECD Convention). The laws of the United States and United Kingdom are then set out as examples of how those Convention standards and requirements are met in two influential jurisdictions. Finally, the law of Canada is set out. Thus, a professor from Africa, Australia, New Zealand or English speaking countries in Asia and Europe has a nearly complete coursebook – for example, that professor can delete the Canadian sections of this book and insert the law and practices of his or her home country in their place. While primarily directed to a law school course on global corruption, this book will be of interest and use to professors teaching courses on corruption from other academic disciplines and to lawyers and other anti-corruption practitioners.
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The Pay for Success Handbook
Suzanne Adatto; Paul Brest · Suzanne Adatto and Paul Brest · 2020
Government agencies frequently contract with nonprofit or for-profit organizations to provide services to improve the well-being of their clients―for example, by reducing recidivism, homelessness, or drug use. Governments have traditionally paid service providers on the basis of the number of clients they treat. The past decade has seen a number of Pay for Success (PFS) or results-based finance (RBF) programs, in which service providers are paid for their outcomes or results. For example, whereas a government agency contracting with a service provider to reduce recidivism among young men released from prison would traditionally have paid the service provider for the hours spent counseling a client, a PFS contract pays the organization for success in reducing the clients’ rate of recidivism from some baseline. This handbook is written for government officials considering the adoption of Pay For Success (PFS) programs and for students in public policy and business schools interested in studying outcomes-oriented government contracts for services. Part One introduces concepts necessary to develop and operate a service delivery program and then surveys some of the issues specific to PFS. Part Two presents two detailed case studies and a number of shorter descriptions of PFS programs. Part Three focuses on the components of PFS programs; it also discusses barriers to their development and ways of overcoming them. An editable file (docx) is also available.