{"data":[{"id":710,"title":"First Semester in Numerical Analysis with Julia","edition_statement":"2.1","volume":null,"copyright_year":2023,"isbn10":null,"isbn13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":"","accessibility_features":[],"description":"First Semester in Numerical Analysis with Julia presents the theory and methods, together with the implementation of the algorithms using the Julia programming language (version 1.1.0). The book covers computer arithmetic, root-finding, numerical quadrature and differentiation, and approximation theory. The reader is expected to have studied calculus and linear algebra. Some familiarity with a programming language is beneficial, but not required. The programming language Julia will be introduced in the book. The simplicity of Julia allows bypassing the pseudocode and writing a computer code directly after the description of a method while minimizing the distraction the presentation of a computer code might cause to the flow of the main narrative.","contributors":[{"id":4855,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Giray","middle_name":null,"last_name":"Ökten","location":"Florida State University","background_text":"Giray Ökten"}],"subjects":[{"id":86,"name":"Analysis","parent_subject_id":7,"call_number":"QA299.6-433","visible_textbooks_count":8,"url":"https://staging.open.umn.edu/opentextbooks/subjects/analysis"},{"id":35,"name":"Applied","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":48,"url":"https://staging.open.umn.edu/opentextbooks/subjects/applied"}],"publishers":[{"id":688,"url":"https://purl.lib.fsu.edu/diginole/FSU_libsubv1_scholarship_submission_1556028278_15938059","year":2020,"created_at":"2019-05-15T18:37:43.000-05:00","updated_at":"2025-08-18T11:19:37.000-05:00","name":"Florida State University"}],"formats":[{"id":1211,"type":"PDF","url":"https://purl.lib.fsu.edu/diginole/FSU_libsubv1_scholarship_submission_1556028278_15938059","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"5","textbook_reviews_count":3,"reviews":[{"id":3591,"first_name":"Sangphil","last_name":"Kim","position":"Assistant Professor","institution_name":"Minnesota State University System","comprehensiveness_rating":4,"comprehensiveness_review":"This book doesn't cover several topics in numerical analysis such as differential equations and eigenvalue if we compare it with conventional textbooks. However, this textbook covers enough topics in numerical analysis for undergraduate students. As you can see in the title, it would be good enough for one semester.","accuracy_rating":5,"accuracy_review":"Content is accurate, error-free and unbiased.","relevance_rating":5,"relevance_review":"Adapting Julia is more than up-to-date. It is proactive.  I don't find anything out-of-date. The necessary updates will be minor or none and easy to implement.","clarity_rating":5,"clarity_review":"One of the strengths of this text is abundant examples. It explains concepts in mathematical expressions and followed by examples with codes.","consistency_rating":5,"consistency_review":"Each chapter is consistent in format, structure as well as terminology.","modularity_rating":5,"modularity_review":"The first chapter introduces Julia which will be used for all the rest chapters. Except for the first chapter, the text has well-divided chapters so that an instructor can change the order of chapters or omit some chapters, without any problem.","organization_rating":5,"organization_review":"The topics in the text are presented in a logical, clear fashion.","interface_rating":5,"interface_review":"The text is free of significant interface issues. Charts and codes are in different colors so that easy to distinguish them from the main text.","grammatical_rating":5,"grammatical_review":"No grammatical errors found.","cultural_rating":5,"cultural_review":"It is very technical. The text can not be culturally insensitive","overall_rating":10,"overall_review":"\"Walk like Python, Run like C\" Julia is a programming language designed for scientific computation. I believe Julia will become one of the major programming languages, especially in Engineering and Quantitative Economics.  I am glad to see an open textbook about Julia so early. I like the book not only because of Julia but also because of the solid mathematics parts.","created_at":"2020-02-18T20:53:10.000-06:00","updated_at":"2020-02-18T20:53:10.000-06:00"},{"id":3800,"first_name":"Yaning","last_name":"Liu","position":"Assistant Professor","institution_name":"University of Colorado Denver","comprehensiveness_rating":4,"comprehensiveness_review":"This book covers the topics of computer arithmetic, iterative methods for nonlinear equations, interpolation methods, numerical quadrature and differentiation, and least squares problems, which are typically discussed in a first course of numerical analysis.","accuracy_rating":5,"accuracy_review":"No errors are found.","relevance_rating":5,"relevance_review":"The book uses a lot of examples that are highly related to the author's research and are not commonly seen in other textbooks, and the rising Julia programming language is used to illustrate the algorithms, both making the book up-to-date and unique.","clarity_rating":5,"clarity_review":"The text reads very well.","consistency_rating":5,"consistency_review":"The book uses consistent terminology.","modularity_rating":5,"modularity_review":"The book divides each topic into a few smaller sections and an instructor can cover each in one or two lectures at their convenience.","organization_rating":5,"organization_review":"The organization of the topics is logical and clear.","interface_rating":5,"interface_review":"The book uses a lot of high-quality figures to help understand the material, without distracting the reader at all. No navigation problems are found.","grammatical_rating":5,"grammatical_review":"No grammatical errors are found.","cultural_rating":5,"cultural_review":"No culturally offensive examples are found in this book.","overall_rating":10,"overall_review":"The book treats the commonly discussed topics in the first-semester numerical analysis with Julia and uses a lot of unique examples related to the author's research, which provides the readers a fresh experience with learning numerical analysis. I would like to highly recommend using the book.","created_at":"2020-05-05T22:30:37.000-05:00","updated_at":"2020-05-05T22:30:37.000-05:00"},{"id":34917,"first_name":"Namyong","last_name":"Lee","position":"Professor","institution_name":"Minnesota State University Mankato","comprehensiveness_rating":4,"comprehensiveness_review":"The textbook seemed more focused on brief one-semester material. It has the most essential topics in the first course in Numerical Methods for college students. Some other textbooks have a topic in numerical linear algebra which is missing in this textbook. However, as the textbook seems to aim for a brief exposition of the numerical methods for one semester, it serves the goal.","accuracy_rating":4,"accuracy_review":"The textbook's contents, including the theorems, proofs, and examples are concise and accurate.  One of the reasons is that the textbook wisely avoids any complicated part of the proof and exposition by simply mentioning some references.","relevance_rating":5,"relevance_review":"The textbook contents are aligned with standard topics for an introductory course in undergraduate numerical methods class.  These topics didn't change for a long time.","clarity_rating":5,"clarity_review":"The main advantage of the textbook is the brief but clear exposition of the topics. To achieve this goal, the author bravely skipped many proofs and lengthy development of the topics.","consistency_rating":5,"consistency_review":"Overall, the textbook is internally consistent and field-tested to achieve this goal. I don't see any unnatural part of the textbook from the consistency of the terminologies and frameworks in the textbook.","modularity_rating":5,"modularity_review":"The textbook is already very brief (about 220 pages) to be covered in a semester (15 weeks) course but can be adequate for a quarter (10 weeks) term situation. Each chapter (from 2 to 5) is quite independent and as a result, one may skip a chapter without much trouble.","organization_rating":5,"organization_review":"The textbook is written in a standard and logical order. I may suggest that the author may add a few samplers or concrete applications in the introduction chapter to give a more clear overview for students.  (From an instructor's perspective, it is not a problem. However, if the introduction part is not interesting, often students stop to read the textbook any further.)","interface_rating":5,"interface_review":"The textbook does not have any serious interface issues as it is the standard PDF format. Every detail is presented clearly in the PDF reader.  My only suggestion is the author provides sample code in the textbook also on a website, such as GitHub. That would benefit students to play with the sample code.","grammatical_rating":5,"grammatical_review":"The textbook is written concisely and clearly to the reader. Each sentence and topic exposition is brief and grammatically correct.  It was easy to read most of the parts of the textbook.","cultural_rating":5,"cultural_review":"I don't find any part of the textbook material culturally insensitive or offensive. Indeed, one feature I like about the textbook is the author introduces a comic character (Arya, followed by the author's daughter's name) and uses it as a gentle introduction to the application problems.","overall_rating":10,"overall_review":"As I briefly mentioned in the above questionnaires, I may suggest strengthening the introduction chapter with more applications and examples.  Also, posting the sample code to GitHub in the form of the Jupyter Notebook would benefit students.","created_at":"2024-03-04T20:11:42.000-06:00","updated_at":"2024-03-04T20:11:42.000-06:00"}],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/first-semester-in-numerical-analysis-with-julia","updated_at":"2025-08-18T11:19:37.000-05:00"},{"id":925,"title":"First Semester in Numerical Analysis with Python","edition_statement":null,"volume":null,"copyright_year":null,"isbn10":null,"isbn13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":["unknown"],"description":"The book is based on “First semester in Numerical Analysis with Julia”, written by Giray Ökten. The contents of the original book are retained, while all the algorithms are implemented in Python (Version 3.8.0). Python is an open source (under OSI), interpreted, general-purpose programming language that has a large number of users around the world. Python is ranked the third in August 2020 by the TIOBE programming community index, a measure of popularity of programming languages, and is the top-ranked interpreted language. We hope this book will better serve readers who are interested in a first course in Numerical Analysis, but are more familiar with Python for the implementation of the algorithms. The first chapter of the book has a self-contained tutorial for Python, including how to set up the computer environment. Anaconda, the open-source individual edition, is recommended for an easy installation of Python and effortless management of Python packages, and the Jupyter environment, a web-based interactive development environment for Python as well as many other programming languages, was used throughout the book and is recommended to the readers for easy code development, graph visualization and reproducibility.","contributors":[{"id":5298,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Yaning","middle_name":null,"last_name":"Liu","location":"University of Colorado Denver","background_text":"Yaning Liu, Department of Mathematical and Statistical Sciences - University of Colorado Denver"}],"subjects":[{"id":3,"name":"Computer Science","parent_subject_id":null,"call_number":"QA76","visible_textbooks_count":137,"url":"https://staging.open.umn.edu/opentextbooks/subjects/computer-science-information-systems"},{"id":86,"name":"Analysis","parent_subject_id":7,"call_number":"QA299.6-433","visible_textbooks_count":8,"url":"https://staging.open.umn.edu/opentextbooks/subjects/analysis"},{"id":59,"name":"Programming Languages","parent_subject_id":3,"call_number":"QA76","visible_textbooks_count":26,"url":"https://staging.open.umn.edu/opentextbooks/subjects/programming-languages"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://staging.open.umn.edu/opentextbooks/subjects/mathematics"}],"publishers":[{"id":904,"url":"http://digital.auraria.edu/air","year":null,"created_at":"2020-10-18T21:09:50.000-05:00","updated_at":"2020-10-18T21:13:20.000-05:00","name":"Auraria Institutional Repository"}],"formats":[{"id":1827,"type":"PDF","url":"http://digital.auraria.edu/IR00000195/00001/citation","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":2,"reviews":[{"id":4659,"first_name":"Chad","last_name":"Westphal","position":"Professor of Mathematics and Computer Science","institution_name":"Wabash College","comprehensiveness_rating":4,"comprehensiveness_review":"The topics covered by the book are overall appropriate and presented at a reasonable level for undergraduate students with a background in calculus, linear algebra, and programming.  It gives a brief introduction to python, which would be sufficient for a student with some programming experience.  The numerical analysis concepts are often explained through worked (and narrated) examples implemented in python.  This pragmatic approach generally works well, though there are times where specific implementation issues crowd out the fundamental idea at issue.  On the spectrum between an implementation-focused numerical methods course and a theorem-proof numerical analysis course, this text is definitely more on the methods end.  \r\n\r\nThe range of topics is limited for a typical robust undergraduate course in numerical analysis.  There is no coverage of numerical methods for differential equations or numerical linear algebra.  There are some exercises given throughout the text, and these are often implementation/computation focused.  An instructor using the text for a course will likely want to supplement the text with additional exercises, assignments, and/or projects.","accuracy_rating":4,"accuracy_review":"The text of the main body of the book is generally clear and error-free.  The index has references to code in Julia, where it should be to python.  (This seems to be an artifact of the conversion of the original text that used the programming language Julia).","relevance_rating":5,"relevance_review":"The general subject matter is very relevant to a wide range of disciplines and is unlikely to lose relevance soon.  The design of the text incorporates python code throughout the text, so the shelf-life of the book is closely tied to how the language evolves.  It will certainly be possible to update examples, code implementations, etc., though not trivially.","clarity_rating":4,"clarity_review":"The tone of the presentation is generally straightforward and uses typical, concise mathematical conventions.  As a stand-alone reference for a student working alone, it is light on providing motivation and context for the subject.  As such, this book is better suited as a course text, where the experienced instructor can provide some of this additional framing.\r\n\r\nThe book gives several extended example applications posed with the recurring fictional student Arya.  These sections do add some levity to the narrative, but can also be a little distracting.  Sometimes they are used as motivation to introduce a new topic, and in other places as a way to illustrate a specific problem.  The overall readability of the text would be more clear if these sections were delineated more consistently (... are we still helping Arya understand her problem now, or have we moved on to a new topic?)","consistency_rating":4,"consistency_review":"Overall the text uses consistent and appropriate terminology throughout.  However, it could do a better job of distinguishing between rate and order of convergence.  It uses big-O notation somewhat inconsistently throughout.","modularity_rating":5,"modularity_review":"For the subject matter it is reasonably modular.  Much of the material is inherently hierarchical, so there would be little motivation for wanting to rearrange sections.  That said, there are a few sections that can be skipped, which is quite appropriate for an advanced undergraduate text.  As noted above, it would be helpful to have chapters on numerical ODEs and/or numerical linear algebra.","organization_rating":5,"organization_review":"The organization of the text is appropriate for the subject and the depth of coverage.","interface_rating":5,"interface_review":"There is appropriate use of hypertext links in the pdf version, and these work well.  The typesetting, images, and referencing are all done well.  Switching between the main text and imbedded python code could be improved if the code were more visually offset (perhaps a light gray background?).","grammatical_rating":5,"grammatical_review":"No grammar or copy edit issues were noted.","cultural_rating":5,"cultural_review":"There is nothing in this book that can be considered culturally insensitive.","overall_rating":9,"overall_review":"There are many forms that a first course in numerical analysis can take, with relative emphasis on different aspects of the field (implementation, empirical testing, applications, theory, etc.).  This book could be a good component of a course that wishes to focus on implementation in python and doesn't need to cover topics beyond rootfinding, interpolation and numerical integration/differentiation.","created_at":"2021-02-27T11:56:39.000-06:00","updated_at":"2021-02-27T11:56:39.000-06:00"},{"id":34143,"first_name":"Amanda","last_name":"Kis","position":"Lecturer","institution_name":"University of Oklahoma","comprehensiveness_rating":5,"comprehensiveness_review":"The text covers fundamental topics (root-finding, interpolation, numerical quadrature and differentiation, approximation) to give students taking their first course in numerical analysis a good survey of the types of issues they will encounter. While other useful and common topics could have been included, the selection provided keeps the length of the text appropriate for a one-semester introductory course. Each topic has good coverage, providing theory/background as well as motivating examples with solutions and, when applicable, Python code. A good number of additional exercises are provided, which a teacher could assign. This text could work well as the supporting text for a first semester course in numerical analysis with Python.","accuracy_rating":5,"accuracy_review":"I did not find inaccuracies.","relevance_rating":4,"relevance_review":"The text provides example code written in Python 3.8 and makes use of the NumPy, pandas, SciPy, and Matplotlib libraries. Code and outputs as they would appear within a Jupyter notebook environment, including plots and screenshots, are provided. These can be followed and applied even if the reader does not choose to install Anaconda or code within Jupyter notebooks.\r\nFor the topics and example applications covered, it seems unlikely that updates to Python would significantly affect the code shown. If these libraries and especially the Jupyter notebook interface are updated, larger edits might be required to keep the text relevant. The structure of the text would allow for new code, plots, and screenshots to replace older examples, although this could be a time-consuming process depending on the updates.\r\nThe topics covered in the text likely will remain relevant, as will the use of Python and these scientific libraries. Jupyter notebooks currently are a commonly used educational tool. If another tool reaches similar levels of popularity, the text might need significant updates.","clarity_rating":5,"clarity_review":"The text is written in a straightforward manner and includes many mathematical and coding examples to support understanding and learning. Students can compare their code to the provided examples.\r\nSome theorems include proofs, while others refer to external sources for proofs. Others are not proved within the text, which might be frustrating to a reader, but in general this seems like an appropriate choice since (1) this is not a math textbook and (2) the proofs can be found elsewhere.\r\nThe text assumes the reader has taken all or nearly the full sequence of calculus and is familiar with Python.","consistency_rating":5,"consistency_review":"The text's organization and format are consistent, and appropriate labels for sections/subsections make it easy to follow and navigate. The adventures of a college student (Arya) are used to introduce and motivate topics, which adds some fun as well as provides continuity.","modularity_rating":5,"modularity_review":"A reader can skip to their chapter of choice and find understandable, relevant information that is well-introduced and does not require referring back to previous chapters of the text. In general, definitions and theorems are provided as needed so the reader does not need to scroll back to find them. Sections and sub-sections are labeled in a logical way, and their number is appropriate, so the reader can find and jump to their topic of choice. In general, a teacher could rearrange the way they present the topics and still be supported by this text.","organization_rating":5,"organization_review":"The organization of the text is clear and logical. The text starts with a review of basic calculus and Python concepts that are used throughout the book, which nicely prep the reader for the bulk of the text. Topics approximately are presented in increasing order of difficulty, which could help teachers organize their semester.","interface_rating":5,"interface_review":"I am able to navigate the table of contents within the PDF. Example code and plots are integrated effectively, and plots are sized and scaled appropriately and simple. Equations also are integrated clearly. The index is useful, while I did not try every topic, seems to link back to the appropriate portions of the text correctly.","grammatical_rating":5,"grammatical_review":"I did not find noticeable grammatical errors.","cultural_rating":5,"cultural_review":"I did not find such issues.","overall_rating":10,"overall_review":"I think this would work well as the text for a first semester course in numerical analysis, and Python lends itself well to the tasks and to advanced beginner and intermediate learners.\r\nIf a reader has little experience with Python, that they will need to supplement their learning with other tutorials. Since the book assumes the reader is familiar with Python, the reader would have to go beyond the subsection on Python basics to get up to speed.","created_at":"2022-11-13T11:07:08.000-06:00","updated_at":"2022-11-13T11:07:08.000-06:00"}],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/first-semester-in-numerical-analysis-with-python","updated_at":"2025-12-15T02:31:01.000-06:00"},{"id":463,"title":"A Primer of Real Analysis","edition_statement":null,"volume":null,"copyright_year":2009,"isbn10":null,"isbn13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":["unknown"],"description":"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.","contributors":[{"id":4228,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Dan","middle_name":null,"last_name":"Sloughter","location":"Furman University","background_text":"Dan Sloughter has been teaching Furman students since 1986, and became Professor of Mathematics in 1996. He previously served as an assistant professor at Santa Clara University from 1983-86, and at Boston College from 1981-83. He was also an instructor at Dartmouth College from 1979-81."}],"subjects":[{"id":86,"name":"Analysis","parent_subject_id":7,"call_number":"QA299.6-433","visible_textbooks_count":8,"url":"https://staging.open.umn.edu/opentextbooks/subjects/analysis"},{"id":35,"name":"Applied","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":48,"url":"https://staging.open.umn.edu/opentextbooks/subjects/applied"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://staging.open.umn.edu/opentextbooks/subjects/mathematics"}],"publishers":[{"id":386,"url":"http://www.synechism.org/wp/a-primer-of-real-analysis/","year":null,"created_at":"2018-09-07T12:22:39.000-05:00","updated_at":"2020-01-02T22:42:15.000-06:00","name":"Dan Sloughter"}],"formats":[{"id":665,"type":"PDF","url":"http://synechism.org/primer/primer-real-analysis.pdf","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":1,"reviews":[{"id":3170,"first_name":"Seonguk","last_name":"Kim","position":"Assistant of Professor of Mathematics","institution_name":"DePauw University","comprehensiveness_rating":4,"comprehensiveness_review":"This book consists of all essential sections that students should know in the class, Analysis or Introduction of Real Analysis. First, in chapter 1, it has crucial prerequisite contents. Second, from chapter 2 to  8, the order of sections is reasonable and well-organized. But some instructors may skip chapters, 3, 4 and 8 because of the limit of time.  Finally, I like the composition adding the exercises after the theorems because the student may be able to have ideas much easier.","accuracy_rating":4,"accuracy_review":"The content looks good and little error. Even though some notations are ambiguous and not easily understandable, overall is good.\r\n","relevance_rating":4,"relevance_review":"In the class, Analysis, students learn about the fundamental mathematical structures and concepts, and the related textbook also does not have any space adding the up to date contents. Nevertheless, I feel that this textbook provides a new view of the concepts.  \r\n","clarity_rating":5,"clarity_review":"All text is from the mathematics terminology that makes the writing lucid and readable. ","consistency_rating":5,"consistency_review":"In every chapter, it has used consistent letters and terminologies. Also, the composition is uniform using the order, \r\n1. A brief description of the concepts, \r\n2. Related definitions\r\n3. Theorems\r\n4. Examples\r\n5. Exercise students should think about more. ","modularity_rating":5,"modularity_review":"The book breaks into separated sections, and each part is short and consists of readable and accessible text. \r\n","organization_rating":3,"organization_review":"The order of topics is in general. But it depends on the instructors. For example, I like to introduce the basic concepts, sets including cardinality (chapter 3), functions, logics before starting the sequences. Also, I have explained the idea, topology (chapter 4). So, in my opinion, it is better to organize the order of topics from fundamentals, including cardinality to more functions and to add the appendix, topology. ","interface_rating":5,"interface_review":"\r\nThis text has a lot of essential and useful figures and formulas. I believe the figures and graphs make students understand more easily. ","grammatical_rating":5,"grammatical_review":"It looks no grammatical errors.  At least, I could not find them.","cultural_rating":5,"cultural_review":"This textbook is for pure mathematics. So, I believe it has no inclusive issues about races, ethnicities, and backgrounds at all.","overall_rating":9,"overall_review":"Overall, the textbook is very well-organized. I like the way how to organize the chapters. It is essential and nothing of unnecessary sections. Specifically, I like the composition adding the exercises after theorems and examples. If I use the book, I do not have to add more examples and suggest the students with the exercise problems. There are also some drawbacks to the book like ordering the topics.  Nevertheless, I value this book in teaching the course Analysis.","created_at":"2019-09-20T09:06:04.000-05:00","updated_at":"2019-09-20T09:06:04.000-05:00"}],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/a-primer-of-real-analysis","updated_at":"2025-12-15T02:09:02.000-06:00"},{"id":243,"title":"Introduction to Mathematical Analysis I","edition_statement":"Second Edition","volume":null,"copyright_year":2016,"isbn10":null,"isbn13":null,"license":"Attribution-NonCommercial","language":"eng","accessibility_statement":"","accessibility_features":[],"description":"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).","contributors":[{"id":3676,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Beatriz","middle_name":null,"last_name":"Lafferriere","location":"Portland State University","background_text":"Beatriz Lafferriere, Assistant Professor, Fariborz Maseeh Department of Mathematics and Statistics, Assistant Chair for Undergraduate Program, Director of Undergraduate Advising, Portland State University. PhD Rutgers University."},{"id":3677,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Gerardo","middle_name":null,"last_name":"Lafferriere","location":"Portland State University","background_text":"Gerardo Lafferriere, Professor, Fariborz Maseeh Department of Mathematics and Statistics, Portland State University. PhD Rutgers University. Area of Specialty: Mathematical Control Theory, Hybrid Systems, Mathematical Biology, Robotics"},{"id":3678,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Mau Nam","middle_name":null,"last_name":"Nguyen","location":"Portland State University","background_text":"Mau Nam Nguyen, Associate Professor, Fariborz Maseeh Department of Mathematics and Statistics, Portland State University. Ph.D. 2007 Wayne State University. Area of Specialty: Variational \u0026 Convex Analysis, Mathematical Optimization, Non-Linear \u0026 Functional Analysis."}],"subjects":[{"id":86,"name":"Analysis","parent_subject_id":7,"call_number":"QA299.6-433","visible_textbooks_count":8,"url":"https://staging.open.umn.edu/opentextbooks/subjects/analysis"},{"id":35,"name":"Applied","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":48,"url":"https://staging.open.umn.edu/opentextbooks/subjects/applied"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://staging.open.umn.edu/opentextbooks/subjects/mathematics"}],"publishers":[{"id":329,"url":"http://pdxscholar.library.pdx.edu/pdxopen/12/","year":null,"created_at":"2018-09-07T12:22:39.000-05:00","updated_at":"2018-09-07T12:22:39.000-05:00","name":"Portland State University Library"}],"formats":[{"id":752,"type":"Online","url":"https://content.library.pdx.edu/files/PDXScholar/mth311/","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":754,"type":"PDF","url":"https://pdxscholar.library.pdx.edu/pdxopen/12/","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":null,"textbook_reviews_count":0,"reviews":[],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/introduction-to-mathematical-analysis-i-second-edition","updated_at":"2025-12-15T02:10:18.000-06:00"},{"id":174,"title":"Introduction to Real Analysis","edition_statement":null,"volume":null,"copyright_year":2013,"isbn10":null,"isbn13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":"","accessibility_features":[],"description":"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.","contributors":[{"id":3663,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"William","middle_name":"F.","last_name":"Trench","location":"Trinity University","background_text":"William F. Trench, Ph.D. Andrew G. Cowles Distinguished Professor, Trinity University (Retired)."}],"subjects":[{"id":86,"name":"Analysis","parent_subject_id":7,"call_number":"QA299.6-433","visible_textbooks_count":8,"url":"https://staging.open.umn.edu/opentextbooks/subjects/analysis"},{"id":35,"name":"Applied","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":48,"url":"https://staging.open.umn.edu/opentextbooks/subjects/applied"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://staging.open.umn.edu/opentextbooks/subjects/mathematics"}],"publishers":[{"id":256,"url":"http://digitalcommons.trinity.edu/mono/7/","year":null,"created_at":"2018-09-07T12:22:38.000-05:00","updated_at":"2021-01-17T11:29:01.000-06:00","name":"A.T. Still University"}],"formats":[{"id":168,"type":"PDF","url":"https://digitalcommons.trinity.edu/mono/7/","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":2228,"type":"LaTeX","url":"https://digitalcommons.trinity.edu/mono/7/","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"5","textbook_reviews_count":1,"reviews":[{"id":35293,"first_name":"Chad","last_name":"Scott","position":"Professor","institution_name":"University of Wisconsin-Superior","comprehensiveness_rating":5,"comprehensiveness_review":"This text comprehensively covers all of the content (and more) in a standard upper division undergraduate course in real analysis.","accuracy_rating":5,"accuracy_review":"It is very accurate with excellent, well constructed proofs and exercises.","relevance_rating":5,"relevance_review":"The text does not stray from the primary subject matter and the nature of the material provides for longevity.","clarity_rating":5,"clarity_review":"Trench (the author) has a very personable way of writing that invites the reader to relax.  Narrative between theorems brings the reader to a point where they are well position to possibly provide proof of the upcoming theorems themselves.  That, coupled with well done but not verbose proof writing style makes the text very clear for undergraduate consumption vs many commercially available texts I have used in the past.","consistency_rating":5,"consistency_review":"The writing style described in the clarity bullet above remains throughout the text.","modularity_rating":4,"modularity_review":"There is some self reference as is necessary in mathematics.  At times, one needs to refer to previously established lemmas in order to understand proofs being presented in a given section.  But, to the extent possible for mathematics, the material is nicely divided into components most teachers of real analysis would expect.","organization_rating":5,"organization_review":"The text flows nicely in a way that I believe most teachers of real analysis would expect.","interface_rating":5,"interface_review":"The interface is via pdf so the content is very stable.  I've not found any oddly distorted images or cutoff content.  The interface seems very clean.","grammatical_rating":5,"grammatical_review":"I've not found any significant errata.","cultural_rating":5,"cultural_review":"Texts on Real Analysis are a necessary staple for a good undergraduate degree in math.  This text fills that need without any perceptible cultural bias.","overall_rating":10,"overall_review":"I'd love someday to see this book in PreText so that it could be exported to more formats.  It's very well done.","created_at":"2024-10-29T12:06:18.000-05:00","updated_at":"2024-10-29T12:06:18.000-05:00"}],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/introduction-to-real-analysis","updated_at":"2025-12-15T02:01:35.000-06:00"},{"id":95,"title":"Basic Analysis: Introduction to Real Analysis","edition_statement":null,"volume":null,"copyright_year":2016,"isbn10":null,"isbn13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":["unknown"],"description":"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.","contributors":[{"id":3669,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Jirí","middle_name":null,"last_name":"Lebl","location":"Oklahoma State University","background_text":"Jirí Lebl, Assistant Professor, Department of Mathematics, Oklahoma State University."}],"subjects":[{"id":86,"name":"Analysis","parent_subject_id":7,"call_number":"QA299.6-433","visible_textbooks_count":8,"url":"https://staging.open.umn.edu/opentextbooks/subjects/analysis"},{"id":35,"name":"Applied","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":48,"url":"https://staging.open.umn.edu/opentextbooks/subjects/applied"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://staging.open.umn.edu/opentextbooks/subjects/mathematics"}],"publishers":[{"id":50,"url":"http://www.jirka.org/ra/","year":2020,"created_at":"2018-09-07T12:22:36.000-05:00","updated_at":"2021-01-03T17:43:26.000-06:00","name":"Jirí Lebl"}],"formats":[{"id":422,"type":"PDF","url":"https://www.jirka.org/ra/","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":423,"type":"Hardcopy","url":"http://www.lulu.com/shop/jiri-lebl/basic-analysis-introduction-to-real-analysis/paperback/product-21043650.html","price":{"cents":1462,"currency_iso":"USD"},"isbn":null},{"id":1981,"type":"Online","url":"https://www.jirka.org/ra/html/frontmatter-1.html","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":1982,"type":"LaTeX","url":"https://github.com/jirilebl/ra","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":3,"reviews":[{"id":271,"first_name":"William","last_name":"Newton","position":"Research Scientist","institution_name":"Colorado State University","comprehensiveness_rating":5,"comprehensiveness_review":"The textbook covers everything I would want to cover in a course at this level and some more. A teacher can use this book as the sole text of an introductory analysis class and skip the last two chapters for a slower class.","accuracy_rating":4,"accuracy_review":"I found a few minor typographical errors but no serious problems.","relevance_rating":5,"relevance_review":"This is exactly the material that should be covered in an introductory analysis class and it will remain relevant up to date for a long time.","clarity_rating":5,"clarity_review":"The material is presented in a clear, concise manner. Every term is adequately defined.","consistency_rating":5,"consistency_review":"The author does a great job of remaining consistent with terminology throughout the book. ","modularity_rating":5,"modularity_review":"It is difficult to write a highly modular textbook with this material since many results depend on earlier ones. However, this book does as good of a job as could be expected by breaking down the material into reasonable sections and maintaining a consistent numbering scheme throughout the book. When earlier results need to be referenced, they are easy to find.","organization_rating":5,"organization_review":"I am glad that the book opens with set theory. The lack of such material can be a shortcoming of some analysis texts. The chapters are presented in a logical order, with all of the material building on previous results.","interface_rating":5,"interface_review":"I had no trouble reading this book or finding results. I appreciate the use of a consistent numbering scheme for results throughout the textbook.","grammatical_rating":4,"grammatical_review":"I found a few typographical errors, but otherwise everything was fine.","cultural_rating":5,"cultural_review":"This material should be appropriate in any classroom where this subject is being taught. I saw nothing that seemed culturally insensitive. ","overall_rating":10,"overall_review":"This is a great textbook for introductory analysis, and I expect that I will use it the next time I teach the subject.","created_at":"2016-01-07T18:00:00.000-06:00","updated_at":"2016-01-07T18:00:00.000-06:00"},{"id":487,"first_name":"Sonmez","last_name":"Sahutoglu","position":"Associate Professor","institution_name":"University of Toledo","comprehensiveness_rating":4,"comprehensiveness_review":"This text covers all the standard material for a senior level undergraduate (or master level) real analysis class. It start with basics set theory and the real numbers. Then it develops supremum and infimum of bounded sets; limit, limsup, liminf for sequences; series of numbers and functions; continuity and uniform continuity of functions, derivative of functions,  Riemann integral and improper integrals, basics of metric spaces including connectedness, compactness set and continuity of functions between metric spaces. Finally it ends with a proof of fixed point theorem. The text covers all the main theorems (such as mean value theorem, intermediate value theorem, Heine-Borel theorem, Bolzano-Weierstrass theorem, Dini’s theorem) one would expect to be covered in this area. It includes a reasonable number of problems and examples. The text provides an effective index at the end.","accuracy_rating":5,"accuracy_review":"I did not see anything inaccurate.","relevance_rating":5,"relevance_review":"I don't expect the text to be obsolete any time soon as this is an advanced math textbook.","clarity_rating":5,"clarity_review":"The material is presented in a clear fashion and should be very readable by students.","consistency_rating":5,"consistency_review":"The style of the book is very consistent throughout the book.","modularity_rating":4,"modularity_review":"It is as modular as one can expect of a book on this subject. Since everything numbered consistently one can easily find the results needed from the previous chapters.","organization_rating":5,"organization_review":"The material is presented in a logical order. Definitions, theorems, examples, exercises, etc are all numbered in a consistent manner. The book is written in a little bit informal language but that is not a shortcoming.","interface_rating":4,"interface_review":"In general, the interface of this book is very typical of an advanced math textbook. All the statements are numbered  and hyperlinked making navigation very easy.","grammatical_rating":5,"grammatical_review":"Other then few typos I did not see any grammatical errors.","cultural_rating":5,"cultural_review":"This is not an issue for graduate level mathematics books and this book is no exception.","overall_rating":9,"overall_review":"This book has been approved by the  American Institute of Mathematics Open Textbook Initiative. I have used it twice in my classes and have been very happy about it. The author maintains an errata on his website and has been updating the text regularly. I suggest using the latest edition that can be obtained from the authors website.","created_at":"2016-08-21T19:00:00.000-05:00","updated_at":"2016-08-21T19:00:00.000-05:00"},{"id":2525,"first_name":"Jeromy","last_name":"Sivek","position":"Assistant Professor - NTT","institution_name":"Temple University","comprehensiveness_rating":5,"comprehensiveness_review":"This book gives a very thorough coverage from set-theoretic prerequisites to difficult questions of the more advanced topics that students need for Real Analysis.  The proofs are helpfully detailed.  The little tricky parts are not skipped or left to the reader.  A professor trying to demonstrate rigor to their students will appreciate the choices made by the author.\r\n\r\nThe book has a good index and a comprehensive glossary.  The little touches are greatly appreciated.","accuracy_rating":5,"accuracy_review":"The book is well-written and has clearly been scrubbed of simple errors.  This is a book that I used with much success as a very young instructor who needed a solid base of material.  I developed confident that this book had correctly worked examples and proofs.","relevance_rating":5,"relevance_review":"This is exactly the material that a student needs to see in their first two semesters of introductory analysis.  It can be used as a first proof-based course coming after a linear algebra or possibly concurrently.  Different people will find it fitting their curriculum differently.  But this book provides a very nice two semester course that starts by introducing set theory and induction for the first time and ends with students ready for topology, measure theory, or more advanced calculus.","clarity_rating":5,"clarity_review":"The clarity of the writing is appreciated.  As a proof-based math text of course students will need to be guided through reading it.  But the pointers and language are arranged to maximize usability by a faculty person.  Because the book has some volume, an instructor can challenge their students to read some sections independently with confidence that the material is arranged clearly enough, obscured only by the usual challenges related to understanding analysis.","consistency_rating":5,"consistency_review":"This book sticks to its organizing principles.  The definition-example-proof-theorem-exercise setup is tried and true.","modularity_rating":5,"modularity_review":"Sections are broken into subsections in appropriate places.  It is appropriately self-referential in a way that is necessary for a book building up a mathematical theory.  The way in which some sections are optional is explained on the first page of the introduction.","organization_rating":5,"organization_review":"The text builds up the material in a sensible fashion.  Some of the ordering choices are the subject of lively pre-existing lively debates.  But all of the organizational choices here are logical and lead to a workable year if taken on order.","interface_rating":5,"interface_review":"I did not notice any interface issues.","grammatical_rating":5,"grammatical_review":"I do not remember being troubled by any grammatical errors.","cultural_rating":5,"cultural_review":"This book is not culturally insensitive or offensive.  Books in this subject rarely are.","overall_rating":10,"overall_review":"I recommend this book very highly.  I used it with much success as a first proof-based course for sophomore/ junior level students at Pitt.  You should give it a try.","created_at":"2019-01-14T20:52:02.000-06:00","updated_at":"2019-01-14T20:52:02.000-06:00"}],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/basic-analysis-introduction-to-real-analysis","updated_at":"2025-12-15T02:02:10.000-06:00"},{"id":1243,"title":"The Art of Polynomial Interpolation","edition_statement":null,"volume":null,"copyright_year":null,"isbn10":null,"isbn13":null,"license":"Attribution-NonCommercial","language":"eng","accessibility_statement":null,"accessibility_features":["unknown"],"description":"The inspiration for this text grew out of a simple question that emerged over a number of years of teaching math to Middle School, High School and College students. Practically speaking, what is the origin of a particular polynomial? So much time is spent analyzing, factoring, simplifying and graphing polynomials that it is easy to lose sight of the fact that polynomials have a wealth of practical uses. Exploring the techniques of interpolating data allows us to view the development and birth of a polynomial. This text is focused on laying a foundation for understanding and applying several common forms of polynomial interpolation. The principal goals of the text are: Breakdown the process of developing polynomials to demonstrate and give the student a feel for the process and meaning of developing estimates of the trend (s) a collection of data may represent. Introduce basic matrix algebra to assist students with understanding the process without getting bogged down in purely manual calculations. Some manual calculations have been included, however, to assist with understanding the concept. Assist students in building a basic foundation allowing them to add additional techniques, of which there are many, not covered in this text.","contributors":[{"id":5902,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Stuart","middle_name":null,"last_name":"Murphy","location":null,"background_text":"Stuart Murphy spent a number of years working in the insurance industry, managing and implementing health plans for commercial and government entities. During this time, he also served as a registered lobbyist. Over the years Stu has taught middle, high school, and college level math; as well as COBOL and Assembler. Stu currently teaches middle school mathematics. He and his wife Sharon have three children and eight grandchildren. They make their home in Pennsylvania."}],"subjects":[{"id":86,"name":"Analysis","parent_subject_id":7,"call_number":"QA299.6-433","visible_textbooks_count":8,"url":"https://staging.open.umn.edu/opentextbooks/subjects/analysis"},{"id":35,"name":"Applied","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":48,"url":"https://staging.open.umn.edu/opentextbooks/subjects/applied"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://staging.open.umn.edu/opentextbooks/subjects/mathematics"}],"publishers":[{"id":1222,"url":"https://www.psupress.org/","year":null,"created_at":"2022-09-01T12:40:43.000-05:00","updated_at":"2022-09-01T12:40:43.000-05:00","name":"Pennsylvania State University"}],"formats":[{"id":3105,"type":"PDF","url":"https://psu.pb.unizin.org/polynomialinterpretation/open/download?type=pdf","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":3106,"type":"Online","url":"https://psu.pb.unizin.org/polynomialinterpretation/","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":null,"textbook_reviews_count":0,"reviews":[],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/the-art-of-polynomial-interpolation","updated_at":"2025-12-15T02:35:00.000-06:00"},{"id":1320,"title":"Basic Engineering Data Collection and Analysis","edition_statement":null,"volume":null,"copyright_year":2001,"isbn10":null,"isbn13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":"","accessibility_features":[],"description":"In Basic Engineering Data Collection and Analysis, Stephen B. Vardeman and J. Marcus Jobe stress the practical over the theoretical. Step by step, students get real engineering data and scenario examples along with chapter-long case studies that illustrate concepts in realistic, thoroughly detailed situations. This approach encourages students to work through the material by carrying out data collection and analysis projects from problem formulation through the preparation of professional technical reports—just as if they were on the job.","contributors":[{"id":6046,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Steve","middle_name":null,"last_name":"Vardeman","location":"Ames, Iowa","background_text":"Steve Vardeman, Iowa State University"},{"id":6047,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"J. Marcus","middle_name":null,"last_name":"Jobe","location":"Oxford, Ohio","background_text":"J. 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