Digital library
Textbooks, references and open learning resources.
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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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Book of Proof
Richard Hammack · Richard Hammack · 2018
This is a book about how to prove theorems. Until this point in your education, you may have regarded mathematics primarily as a computational discipline. You have learned to solve equations, compute derivatives and integrals, multiply matrices and find determinants; and you have seen how these things can answer practical questions about the real world. In this setting, your primary goal in using mathematics has been to compute answers. But there is another approach to mathematics that is more theoretical than computational. In this approach, the primary goal is to understand mathematical structures, to prove mathematical statements, and even to invent or discover new mathematical theorems and theories. The mathematical techniques and procedures that you have learned and used up until now have their origins in this theoretical side of mathematics. For example, in computing the area under a curve, you use the fundamental theorem of calculus. It is because this theorem is true that your answer is correct. However, in your calculus class you were probably far more concerned with how that theorem could be applied than in understanding why it is true. But how do we know it is true? How can we convince ourselves or others of its validity? Questions of this nature belong to the theoretical realm of mathematics. This book is an introduction to that realm. This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems,explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics. This text has been used in classes at: Virginia Commonwealth University, Lebanon Valley College, University of California - San Diego, Colorado State University, Westminster College, South Dakota State University, PTEK College - Brunei,
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Fundamentals of Math, Physics, and Statistics for Future Transportation Professionals
Anurag Pande; Peyton Ratto; Ahmed Farid · Mavs Open Press · 2024
This textbook and OER material cover tools and basic knowledge required to master the prerequisite essentials of physics, mathematics, and statistics applied in transportation engineering. To our knowledge, no such textbook currently exists to build the KSTs (Knowledge, Skills, Tools) for college freshmen’ remedial courses required by most transportation engineering graduate programs that admit non-engineers (e.g., PHYS 141, MATH 142, STAT 321 at California Polytechnic State University, San Luis Obispo). The textbook modules are intended for students with undergraduate degrees in planning and other less technical fields who are interested in pursuing transportation careers where background engineering knowledge is required. This textbook is a product of the grant OERTransport: Enabling Transportation Planning Professional Advancement awarded to the University of Texas-Arlington (UTA) in consortium with California Polytechnic State University (Cal Poly) and the University of South Florida (USF). It was developed under an Open Textbooks Pilot grant from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education. However, its contents do not necessarily represent the policy of the Department of Education, and no endorsement by the Federal Government should be assumed
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Introduction to Probability
Charles Grinstead; J. Laurie Snell · American Mathematical Society · 2006
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 continuedto 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 scholarlyactivity from music to physics, and in daily experience from weather prediction topredicting the risks of new medical treatments. This text is designed for an introductory probability course taken by sophomores,juniors, and seniors in mathematics, the physical and social sciences, engineering,and computer science. It presents a thorough treatment of probability ideas andtechniques necessary for a form understanding of the subject. The text can be usedin a variety of course lengths, levels, and areas of emphasis. For use in a standard one-term course, in which both discrete and continuousprobability is covered, students should have taken as a prerequisite two terms ofcalculus, including an introduction to multiple integrals. In order to cover Chapter 11, which contains material on Markov chains, some knowledge of matrix theoryis necessary. The text can also be used in a discrete probability course. The material has beenorganized in such a way that the discrete and continuous probability discussions arepresented in a separate, but parallel, manner. This organization dispels an overlyrigorous or formal view of probability and o?ers some strong pedagogical valuein that the discrete discussions can sometimes serve to motivate the more abstractcontinuous probability discussions. For use in a discrete probability course, studentsshould have taken one term of calculus as a prerequisite. Very little computing background is assumed or necessary in order to obtain fullbenefits from the use of the comp
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Yet Another Introductory Number Theory Textbook (Cryptology Emphasis Version)
Jonathan Poritz · Jonathan Poritz · 2014
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.
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Discrete Mathematics for Information Technology
Simon Crothers · Kwantlen Polytechnic University · 2026
Discrete Mathematics for Information Technology is an applied, student-focused introduction to the mathematical foundations that underpin modern computing. Designed for learners in information technology and business contexts, this textbook bridges theory and practice by connecting core concepts, such as number systems, data representation, logic, proofs, relations, algorithms, Boolean algebra, and graph theory, to real-world applications in programming, networking, databases, and systems design. Each chapter is structured with clear explanations, worked examples, case studies, and programming-oriented exercises that reinforce both conceptual understanding and practical skills. Emphasis is placed on developing analytical thinking, problem-solving, and the ability to model and reason about digital systems with precision and confidence. As an open educational resource, the text is adaptable and accessible, supporting a wide range of teaching and learning environments. By integrating mathematical rigor with authentic IT scenarios, this book equips students with the essential tools needed to succeed in modern, data-driven and technology-focused careers.
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Evidence-based Software Engineering
Derek Jones · Knowledge Software · 2020
This book discusses what is currently known about software engineering, based on an analysis of all the publicly available data. This aim is not as ambitious as it sounds, because there is not a great deal of data publicly available. The intent is to provide material that is useful to professional developers working in industry; until recently researchers in software engineering have been more interested in vanity work, promoted by ego and bluster. The material is organized in two parts, the first covering software engineering and the second the statistics likely to be needed for the analysis of software engineering data.
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Introduction to Statistical Thinking
Benjamin Yakir · Benjamin Yakir · 2010
The target audience for this book is college students who are required to learn statistics, students with little background in mathematics and often no motivation to learn more. It is assumed that the students do have basic skills in using computers and have access to one. Moreover, it is assumed that the students are willing to actively follow the discussion in the text, to practice, and more importantly, to think. Teaching statistics is a challenge. Teaching it to students who are required to learn the subject as part of their curriculum, is an art mastered by few. In the past I have tried to master this art and failed. In desperation, I wrote this book. This book uses the basic structure of generic introduction to statistics course. However, in some ways I have chosen to diverge from the traditional approach. One divergence is the introduction of R as part of the learning process. Many have used statistical packages or spreadsheets as tools for teaching statistics. Others have used R in advanced courses. I am not aware of attempts to use R in introductory level courses. Indeed, mastering R requires much investment of time and energy that may be distracting and counterproductive for learning more fundamental issues. Yet, I believe that if one restricts the application of R to a limited number of commands, the benefits that R provides outweigh the difficulties that R engenders. Another departure from the standard approach is the treatment of probability as part of the course. In this book I do not attempt to teach probability as a subject matter, but only specific elements of it which I feel are essential for understanding statistics. Hence, Kolmogorov’s Axioms are out as well as attempts to prove basic theorems and a Balls and Urns type of discussion. On the other hand, emphasis is given to the notion of a random variable and, in that context, the sample space.
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International Finance: Theory and Policy
Steve Suranovic · Saylor Foundation · 2010
International Finance Theory and Policy is built on Steve Suranovic's belief that to understand the international economy, students need to learn how economic models are applied to real world problems. It is true what they say, that ”economists do it with models.“ That's because economic models provide insights about the world that are simply not obtainable solely by discussion of the issues. International Finance Theory and Policy develops a unified model of the international macroeconomy. The text provides detailed descriptions of major macroeconomic variables, covers the interest rate parity and purchasing power parity theories of exchange rate determination, takes an exhaustive look at the pros and cons of trade imbalances and presents the well-known AA-DD model to explore the effects of fiscal and monetary policy under both fixed and flexible exchange rates. The models are developed, not by employing advanced mathematics, but rather by walking students through a detailed description of how a model's assumptions influence its conclusions. But more importantly, each model and theory is connected to real world policy issues. The Finance Text has the following unique features: o Begins with an historical overview of the international macroeconomy to provide context for the theory. o Concludes with a detailed discussion of the pros and cons of fixed and floating exchange rate systems. o Provides an extensive look at the issue of trade imbalances. Readers learn techniques to evaluate whether a country's trade deficit (or surplus) is dangerous, beneficial, or benign. o Explains how purchasing power parity is used to make cross country income comparisons. o Offers clear detailed explanations of the AA-DD model. o Applies the AA-DD model to understand the effects of monetary and fiscal policy on GDP, the exchange rate, and the trade balance. International Finance Theory and Policy by Steve Suranovic is intended for a one-semester course in International Finance. After M
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Introductory Business Statistics
Lex Holmes; Barbara Illowsky; Susan Dean · OpenStax · 2023
Introductory Business Statistics 2e aligns with the topics and objectives of the typical one-semester statistics course for business, economics, and related majors. The text provides detailed and supportive explanations and extensive step-by-step walkthroughs. The author places a significant emphasis on the development and practical application of formulas so that students have a deeper understanding of their interpretation and application of data. Problems and exercises are largely centered on business topics, though other applications are provided in order to increase relevance and showcase the critical role of statistics in a number of fields and real-world contexts. The second edition retains the organization of the original text. Based on extensive feedback from adopters and students, the revision focused on improving currency and relevance, particularly in examples and problems. A detailed transition guide is available for instructors. The first edition of Introductory Business Statistics by OpenStax is available in web view here.
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Introductory Business Statistics with Interactive Spreadsheets
Mohammad Mahbobi; Thomas Tiemann · BCcampus · 2010
Introductory Business Statistics with Interactive Spreadsheets – 1st Canadian Edition is an adaptation of Thomas K. Tiemann's book, Introductory Business Statistics. This new edition still contains the basic ideas behind statistics, such as populations, samples, the difference between data and information, and sampling distributions as well as information on descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics. New topics include the chi-square test and categorical variables, null and alternative hypotheses for the test of independence, simple linear regression model, least squares method, coefficient of determination, confidence interval for the average of the dependent variable, and prediction interval for a specific value of the dependent variable. This new edition also allows readers to learn the basic and most commonly applied statistical techniques in business in an interactive way — when using the web version — through interactive Excel spreadsheets. For each topic, a customized interactive template has been created within which selected values can be repeatedly changed to observe how the entire process, as well as the outcomes, are automatically adjusted. Also, in this adapted edition, the real-world examples throughout the text, and the information in general, have been revised to reflect Canadian content.
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Υπολογιστική Φυσική: Ένα βιβλίο του Κωνσταντίνου Αναγνωστόπουλου
Κωνσταντίνος Αναγνωστόπουλος · National Technical University of Athens · 2016
Το βιβλίο αυτό είναι μια εισαγωγή στις υπολογιστικές μεθόδους που χρησιμοποιούνται στη φυσική και άλλα επιστημονικά πεδία. Απευθύνεται σε κοινό που έχει ήδη εκτεθεί σε μαθήματα γενικής φυσικής που διδάσκονται στα δύο πρώτα έτη πανεπιστημιακών τμημάτων θετικών επιστημών και επιστημών του μηχανικού. Δεν υποθέτει κανένα υπόβαθρο αριθμητικής ανάλυσης, προγραμματισμού ή χρήσης υπολογιστή και παρουσιάζει ό,τι είναι απαραίτητο για την επίλυση των προβλημάτων που παρουσιάζονται στο βιβλίο. Μπορεί να χρησιμοποιηθεί ως κύριο σύγγραμμα σε εισαγωγικά μαθήματα υπολογιστικής φυσικής και επιστημονικού προγραμματισμού. Το βιβλίο ξεκινάει με πολύ απλά προβλήματα πάνω στην κίνηση σωματιδίου και ολοκληρώνεται με μία εις βάθος συζήτηση προχωρημένων μεθόδων προσομοίωσης Μόντε Κάρλο στη στατιστική φυσική. Το επίπεδο διδασκαλίας είναι διαβαθμισμένο ως προς τη δυσκολία του, παρουσιάζοντας προβλήματα όπως η εξίσωση διάχυσης, δυναμικά συστήματα, ηλεκτροστατική στο επίπεδο, κβαντομηχανική και οι τυχαίες διαδρομές. Όλο το υλικό που παρουσιάζεται στο βιβλίο μπορεί να διαδαχθεί άνετα σε δύο εξάμηνα. Με κατάλληλη επιλογή θεμάτων, μπορεί να χρησιμοποιηθεί και σε ένα πλήρες μάθημα ενός εξαμήνου. Το βιβλίο αποσκοπεί να δώσει στους φοιτητές το υπόβαθρο και την εμπειρία που απαιτείται ώστε να προχωρήσουν σε προγράμματα υπολογισμών υψηλής απόδοσης. Δίνει έμφαση στον εμπειρικό προγραμματισμό αριθμητικών προγραμμάτων, αλλά και στην παραγωγή, ανάλυση και φυσική ερμηνεία των δεδομένων. Επίσης γίνεται προσπάθεια να διατηρηθεί το ενδιαφέρον του αναγνώστη μέσα από την παρουσίαση της αριθμητικής επίλυσης γνωστών και ενδιαφέροντων προβλημάτων φυσικής, οπως χαοτικών συστημάτων, κβαντομηχανικής, ειδικής θεωρίας της σχετικότητας και της φυσικής των μεταβάσεων φάσης. Το βιβλίο και το συνοδευτικό λογισμικό δίνονται ελεύθερα, αδειοδοτούμενα υπό Creative Commons License/GNU public License.
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Calculo diferencial e integral
Marta Bonacina; Claudia Teti; Alejandra Haidar · LATIn Project · 2014
Esta comunidad tiene como fin construir un texto base, que pretende ser la puerta de entrada al mundo de las matemáticas superiores y sus aplicaciones en el campo de las Ciencias de la Ingeniería.