Mitch's Reading List

If you were looking for my annotated bibliography, then you are in the right place. I have switched over my personal bibliography software, and am very slowly populating this list from that source.

Stevens, W Richard. Advanced Programming in the UNIX® Environment. 3rd ed., n.d.

This is an update of an absolute classic, and the definitive guide for UNIX programmers. Rago has done an excellent job updating this work to include topics important to modern UNIX programmers like POSIX threads. He has also done a masterful job updating the standards related material including updating all the examples and discussions for newer APIs. He has maintained the incredibly readable style of the original work. This is an absolute must have for any programmer that touches a UNIX system. I even recommend this book to UNIX admins and users. Go out and buy this book!

Das, Anadijiban, and Andrew DeBenedictis. The General Theory of Relativity. New York ; London: Springer, 2012.

My current favorite book on general relativity.

Bambi, Cosimo. Introduction to General Relativity. Undergraduate Lecture Notes in Physics. Singapore: Springer Singapore, 2018.

This is probably the best introduction to the subject I have come across in a long time. It's a great first book.

Trappe, Wade, and Lawrence C. Washington. Introduction to Cryptography: With Coding Theory. 2nd ed. Upper Saddle River, N.J: Pearson Prentice Hall, 2005.

This has got to be the most approachable cryptography book available today that actually discusses real cryptography. May books exist today that say they are about cryptography, but are completely absent of any mathematics. This is NOT such a book. The writing is very clear and easy to follow. The proofs are easy to read and are rigorous. The exercises and examples are well thought out and numerous. The additional material on coding theory forms a good, but short, introduction to that subject. This book could be used by undergraduates with little preparation but some mathematical maturity. This book won't make you an expert, but it is a great introduction and a fun read.

Stinson, Douglas R. Cryptography: Theory and Practice. 3rd ed. The CRC Press Series on Discrete Mathematics and Its Applications. Boca Raton: Chapman & Hall/CRC, 2006.

This book forms a good introduction to cryptography and protocols for the beginner. This book has a little bit of math, a little bit of practice, and some very good examples. For example, this book actually has a worked example with real data for DES – a real boon for someone trying to implement and understand the algorithm for the first time. The writing is quite clear and the math is well thought out with an eye to making sure that beginners will understand. This book is more practical than Trappe's book but less practical than Schneier's book for the modern software developer or user of cryptography.

Schneier, Bruce. Applied Cryptography: Protocols, Algorithms, and Source Code in C. 2nd ed. New York: Wiley, 1996.

This well written work is an applied introduction to basic cryptography protocols and algorithms. The book's focus is on appropriate use of cryptographic systems as well as on the commonly used algorithms encountered today. The book is littered with source code (in C) and examples. It is probably the most readable book on basic cryptography use available today. This book doesn't provide a rigorous mathematical treatment, it is for the semi-technical user of cryptography not for the cryptographer. It is a bit dated, but most of the material still holds up.

Foley, James D., ed. Computer Graphics: Principles and Practice. 2nd ed. in C. Addison-Wesley Systems Programming Series. Reading, Mass: Addison-Wesley, 1995.

This is, without question, the best general computer graphics book I have ever found. The writing is very clear. The selection of topics is comprehensive, and quite deep in parts. For example, the coverage of scan line conversion is by far the best to be found The code examples are in C, and very readable. A large number of well thought out exercises are provided. This work can be used as a text book or for self study. If you own only one computer graphics book, then this is the one to own. Note this is the 2nd edition – do not get the 3rd edition!

Sayood, Khalid. Introduction to Data Compression. 4th ed. Waltham, MA: Morgan Kaufmann, 2012.

This is the best book I have found about data compression. It is well written, easy to understand, comprehensive, and well organized. The book is full of examples, and has a few exercises – it could be used as a text book. The selection of topics covers classical compression as well as more modern compression algorithms After reading this book one should be able to implement workable compression code, or at least work on compression code.

Salomon, D. Data Compression: The Complete Reference. 4th ed. London: Springer, 2007.

This comprehensive reference covers most of the compression methods you are likely to meet in the real world.

Casselman, Bill. Mathematical Illustrations. Cambridge ; New York: Cambridge University Press, 2005.

This great little book explores the world of creating mathematical illustrations via direct use of the Postscript language. Postscript allows for some simple and elegant solutions to some of the difficult illustration problems mathematical authors face. This text is a very good introduction to some of the most useful techniques, and to the postscript language in general. An electronic copy of the book is available at the author's web site.

Lamport, Leslie. LATEX: A Document Preparation System: User’s Guide and Reference Manual. 2nd ed. Reading, Mass: Addison-Wesley Pub. Co, 1994.

This book is the de-facto standard user guide and reference manual for the LaTeX system written by the guy who wrote the system. This is a very readable work. This is just an introduction.

Mittelbach, Frank, Michel Goossens, Johannes Braams, and Chris Rowley. The LaTeX Companion. 2nd ed. Addison-Wesley Series on Tools and Techniques for Computer Typesetting. Boston: Addison-Wesley, 2004.

A great second book on LaTeX.

Peitgen, Heinz-Otto, and Dietmar Saupe, eds. Science of Fractal Images. Springer-Verlag New York, 2012.

Very strongly recommend for anyone who actually wants to use a computer to generate pictures. This book has an all star group of contributing authors.

Gleick, James. Chaos: Making a New Science. 20th anniversary ed. New York, N.Y: Penguin Books, 2008.

A very interesting introduction to the history of Chaos. This book has almost no mathematics or formal material regarding Fractals or dynamical systems, but is well worth the read for the historical perspective.

Strogatz, Steven Henry. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Cambridge, Mass: Perseus Books, 2001.

This book is a good, well written, basic introduction to dynamical systems. The math is very basic, and the focus of the text is applications to various scientific and engineering fields. This is not a book for a mathematician.

Peitgen, Heinz-Otto, H. Jürgens, and Dietmar Saupe. Chaos and Fractals: New Frontiers of Science. 2nd ed. New York: Springer, 2004.

A good, encyclopedic, introduction to the field in general. This book is notable because of it's clear presentation and breadth of coverage. It's a great book to have around for the casual reader because it is broken up into semi self-contained sections that one can just pick up and read.

Mike Field and Martin Golubitsky. Symmetry in Chaos: A Search for Pattern in Mathematics, Art, and Nature. 2nd ed. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2009.

This is a fantastic book – one worthy of getting in print just for the images. More impressively it describes the methods used to generate the art in enough detail to allow the reader to implement software to create similar works. The authors have some software to get you started on sourceforge.

Ireland, Kenneth, and Michael Ira Rosen. A Classical Introduction to Modern Number Theory. 2nd ed. Graduate Texts in Mathematics 84. New York, NY: Springer, 2010.

Perhaps the best introduction to number theory available today. The treatment is rigorous, concise, well organized, and readable – but a bit symbol heavy. The presentation is quite formal in typical theorem-proof format with few examples, but the proofs very readable and favor simplicity and elementary techniques whenever possible. The level of mathematical maturity required is that of a first year graduate student or well prepared undergraduate. The exercise sets are interesting, well structured and provide good reinforcement of the material.

Koblitz, Neal. A Course in Number Theory and Cryptography. 2nd ed. Graduate Texts in Mathematics. New York Berlin Paris: Springer, 1994.

This is a truly wonderful introduction to computational number theory and mathematical cryptography. It is showing a bit of age, but the presentation is absolutely fantastic. While the work is is intended for the graduate student, this text well written enough that it is approachable by any well prepared and motivated student. The material is well organized, and the mathematical treatment is rigorous. The text has numerous well motivated examples, and a large number of excellent exercises. A true modern classic.

Crandall, Richard E., and Carl Pomerance. Prime Numbers: A Computational Perspective. 2nd ed. New York, NY: Springer, 2005.

This text is not a theoretical mathematics book, but an advanced exposition algorithms for prime number computations – some relatively modern (circa 2000). The text is clearly written and organized. It may be successfully used by a range of readers from those wishing to to understand the way algorithms work at an intuitive level to readers simply wishing to use it in a cookbook fashion to quickly implement various algorithms. While this is not a theoretical text, the authors have still taken pains to be very careful mathematically in the presentation of the material. At the same time they present significant quantities of "meta-mathematical" material designed to impart an intuitive grasp of the subject as well. The examples are topical and reinforce an understanding of the material. The exercises are numerous and range from simple problems to research level material suitable for a PhD thesis. This is a must own for any computational number theorist or anyone interested in prime number computations.

David M. Bressoud. Factorization and Primality Testing. New York: Springer New York, 1989.

This well written and readable book covers the basics of primality testing algorithms ranging from trial division and the sieve of Eratosthenes to elliptic curve techniques. The presentation is elementary and aimed at the novice with little or no background in number theory. While somewhat out of date, the material is still relevant for the target audience. The focus is on describing and explaining the operation of algorithms, and not on the theory behind them. There are many relevant and useful examples as well as explicitly presented algorithms in pseudo-code. The exercises don't provide much depth and are not particularly plentiful. This is great book for the non-mathematician looking for an accessible introduction to number theory and primality testing.

Artin, Michael. Algebra. 2nd ed. Boston, MA: Pearson Education, 2011.

This is a standard text book used for one or two semester abstract algebra classes at the BS and MS levels – it is not appropriate for a PhD class. The selection of topics is sufficient to give a student all the preparation necessary for continued study at the PhD level or before reading a more advanced text. More topics are covered than what is typically found in many BS level algebra texts. The exposition is quite clear and mathematically rigorous. This is an fine choice as a first algebra text. If you only own one basic abstract algebra text, then this one is a good choice.

Hungerford, Thomas W. Algebra, 1980.

This book, like Serge Lang's algebra book, is a standard graduate text forming the core of many one or two semester PhD algebra classes. Like Lang's book, this one covers enough material to fill all the requirements most non-specialists will ever have. This text is clearly written, has good exercises, and provides a rigorous treatment of the included material. It forms a fine second text as a continuation of Hungerford's less advanced algebra book. In my personal opinion, this book is less difficult to read than Lang's, and it also forms a better reference book to keep on your shelf. On the down side, this book doesn't deliver the enthusiasm the subject deserves (read Jacobson's book for that!).

Jacobson, Nathan. Basic Algebra I. 2nd ed., Dover ed. Dover Books on Mathematics. Mineola, N.Y: Dover Publications, 2009.

Jacobson, Nathan. Basic Algebra II. 2nd ed., Dover ed. Dover Books on Mathematics. Mineola, N.Y: Dover Publications, 2009.

This graduate text could form core of a one or two semester algebra class at the MS or PhD level. It is wonderfully well written; however, the exposition is decidedly different from the typical graduate math text. Instead of the typical theorem/proof format, a more narrative approach is taken. Some readers may find this approach difficult or unsettling, but I personally find it quite appealing and easy to read. The treatment is still quite rigorous with formal statements of theorems and proofs given. Reading this book feels like having a conversation with an expert. Everyone will find some new tidbit or insight from a careful read of this book.

Lang, Serge and Springer Science+Business Media. Algebra. Revised. New York: Springer, 2005.

This standard, graduate text forms the core of many required, PhD algebra classes. It is relatively clearly written, the presentation is rigorous, and the selection of topics is appropriate to give the reader a useful breadth of knowledge. This one text is probably enough material to serve the needs of most non-experts. Several other options exist including more readable works by Jacobson and Hungerford. Not recommended as a first abstract algebra text.

Rotman, Joseph. An Introduction to the Theory of Groups. 2nd ed. New York, NY: Springer New York, 1995.

This is THE book to have on group theory. The selection of topics is comprehensive, the organization is absolutely excellent, and the exposition is beyond equal. The presentation is rigorous, but a few gaps and errors exist in both proofs and exercises. The exercises are well thought out, but not as difficult as one would expect for a book like this. This book contains enough material to satisfy most non-specialists. The book is completely self contained and could be used as the text for an undergraduate class, but has enough material and depth for a graduate class as well.

Cox, David A., John B. Little, and Donal O’Shea. Ideals, Varieties, and Algorithms. 4th ed. Undergraduate Texts in Mathematics. Cham Heidelberg New York Dordrecht London: Springer, 2015.

This book is completely understandable by an undergraduate math major with little or no background in abstract algebra. Without a doubt this is one of the best written and easy to understand books about commutative algebra available today. It is not the most complete work because of the intended audience. In keeping with that audience the work has a large number of elementary examples reinforcing the material. The exercise sets are large and appropriate for the intended audience, but also contain a few exercises for more advanced readers. This is the perfect book for the non-mathematician or looking for a good introduction to the subject.

Adams, William W., and Philippe Loustaunau. An Introduction to Gröbner Bases. Graduate Studies in Mathematics, v. 3. Providence, R.I: American Mathematical Society, 1994.

This book is an excellent introduction to the subject of Grobner bases. The intended audience has a mathematical maturity level typical of a beginning graduate student. The selection of topics is quite limited, but the exposition is very clear, concise and rigorous. The text has a generous peppering of useful examples as well as a substantial number of exercises. The exercise sets range in difficulty from trivial to quite challenging.

Becker, Thomas, and Volker Weispfenning. Gröbner Bases: A Computational Approach to Commutative Algebra. New York, NY: Springer New York, 1993.

This is a very comprehensive introduction to Grobner bases suitable for the reader with a solid preparation in graduate level abstract algebra. Little knowledge of commutative algebra a prerequisite for this text. The selection of topics is quite comprehensive, and the presentation is clear and rigorous. Well thought out examples are sprinkled throughout the text as required. The exercise sets are well designed, interesting and thought provoking. This is an excellent book for use as a text for for independent study.

Milovanović, G. V., Dragoslav S. Mitrinović, and Themistocles M. Rassias. Topics in Polynomials: Extremal Problems, Inequalities, Zeros. Singapore ; River Edge, NJ: World Scientific, 1994.

This is a truly wonderful book about polynomials that contains many results that are quite difficult to find elsewhere. The exposition is a bit terse, but always clear and rigorous. The organization is well thought out, and the use of notation and terminology is consistent throughout the work. The exercises range from easy to very challenging, and a few real gems.

Prasolov, V. V. Polynomials. Algorithms and Computation in Mathematics, v. 11. Berlin ; New York: Springer, 2004.

Prasolov's book is one of the best books on general polynomial theory available today. The topics are carefully selected from the vast theory of polynomials, and are masterfully woven together into a cohesive tapestry providing a good view of the overall landscape of the subject. Unfortunately the amount of material covered necessitates rather shallow coverage of many topics, but the shallow areas are accompanied by high quality suggestions for additional reading. The presentation is always clear and rigorous. The exercises are interesting. This one is a real page turner, and is hard to put down.

Rahman, Qazi Ibadur, and Gerhard Schmeisser. Analytic Theory of Polynomials. London Mathematical Society Monographs, new ser., 26. Oxford : New York: Clarendon Press ; Oxford University Press, 2002.

Unlike most works on polynomials, this one focuses entirely on the analytic aspects of the theory. The exposition absolutely top notch in that it is simultaneously readable and rigorous – suitable for self study or classroom use. The work is well enough organized that it may be used as a reference. Notation and terminology intelligently and consistently used throughout the work.

Peterson, W. Wesley, and E. J Weldon. Error Correcting Codes. Massachusetts: MIT Press, 1972.

This book, even while a bit old, is the best introduction to error correcting codes that has ever been written. The coverage of important topics is relatively complete and the organization is masterful. The proofs are easy to understand and are rigorous. The exercise sets are well thought out and reinforce the material quite well. What makes this book special is the exceptionally clear exposition. Few books are this easy to read. This is THE book to own if you want to really understand error correcting codes.

Dugundji, James. Topology. Universal Book Stall, 1990.

This is one of the best introductions to general topology ever written. The exposition is as clear as it gets and the exercises are as well thought out as can be found in any text. Currently this book is out of print, and quite expensive – it is worth the price.

Munkres, James R. Topology. 2nd ed. Upper Saddle River, NJ: Prentice Hall, Inc, 2000.

While Dugundji may be a better book, this one is still in print! Like Dugundji, this book covers enough general topology to take care of the needs of most people. The treatment is rigorous, relatively complete, and very clear.

Satō, Hajime. Algebraic Topology: An Intuitive Approach. Iwanami Series in Modern Mathematics, v. 183. Providence, R.I: American Mathematical Society, 1999.

I wish I had this book when I was learning about algebraic topology for the first time! Each field of mathematics has a canonical set of examples that are used by researchers as guiding lights through the abstract world of mathematics they navigate each day. Algebraic topologists are no different, and this book contains there holy list of examples. Generally speaking it takes most people years of study and interaction with other researchers to internalize a list of guiding examples. This book gives the reader an incredible jump start on that journey. If you are interested in, use as a tool, or are learning algebraic topology or low dimensional topology, then you MUST read this book. If you took an algebraic topology class a decade ago and never really understood it, then read this book! If you think math is cool and just want something fun to look at, then read this book! READ THIS BOOK!

Gelbaum, Bernard R., and John Meigs Hubbell Olmsted. Counterexamples in Analysis. Mineola, N.Y: Dover Publications, 2003.

One of the best ways to really wrap your mind around several topics in real analysis is to consider counterintuitive examples. The best way to understand why all the hypothesis in some of the most important theorems of real analysis are really necessary, is consider what happens when they are violated. This is precisely what this book is about. Exploring the most common counterexamples disproving all of the psudo-theorems students like to invent through blind, incorrect intuition. The selection of examples is excellent and the presentation is clear and precise. This is a great book.

Apostol, Tom M. Mathematical Analysis. 2nd ed. Addison-Wesley Series in Mathematics. Reading, Mass.: Addison-Wesley, 1974.

This book could easily form the basis of a one or two semester advanced calculus or real analysis class for beginning graduate students or advanced undergraduates ready for an introduction to the mathematics that really makes calculus work. It is not appropriate for a PhD level class. In fact, the level of mathematical maturity required to read and understand this book is very low making it a tedious read for advanced students, but a great read for less sophisticated students. The coverage of topics ranges from the traditional undergraduate material intended to add the rigor missing from traditional calculus classes (Riemann integration, series, products, sequences, etc..), to some of the topics traditionally covered in a first graduate analysis class (Lebesgue integration). The presentation is quite precise and rigorous while maintaining a helpful tone for less advanced students. The exercises are plentiful and appropriate. Overall, this is one of the best introductory analysis texts available.

Folland, G. B. Real Analysis: Modern Techniques and Their Applications. 2nd ed. Pure and Applied Mathematics. New York: Wiley, 1999.

This is the most readable treatment of real analysis that I have yet to discover – no small feat considering the number of excellent texts in this area. The exercises are thoughtful and plentiful. The exposition is exceptionally clear, complete, concise, and rigorous. The proofs in this text are exceptionally clear. Common complaints regarding this book are that it is dense and has some typeos – both valid. Overall, I can't recommend this book highly enough!

Rudin, Walter. Real and Complex Analysis. 3rd ed. New York: McGraw-Hill, 1987.

This classic text is rather unique in its class because of its comprehensive treatment of both real and complex analysis. The coverage is extensive enough for this text to serve well as the traditional, two semester PhD level class covering Lebesgue integration. This book could also serve as the basis for a two semester class at the MS level. The exposition is clear, rigorous, and detailed. The exercises are plentiful and thoughtful. This is one of the best written math books of all time.

Royden, H. L, and Patrick Fitzpatrick. Real Analysis. Boston: Pearson Prentice Hall, 2010.

This classic text is great for self study or class work. It is commonly used as a second analysis class at the MS level or a first analysis class at the PhD level. In both cases, it can serve as a one or two semester class. The writing is clear, and the selection of topics is well thought out. The exercises can be quite difficult. The organization is atypical in that integration is discussed before general measure theory; however, I don't necessarily think this is a bad thing even if it leads to some repetition of material. The prerequisites are quite low and include a basic analysis class covering the theoretical aspects of Riemann integration.

Munkres, James R. Analysis on Manifolds. Advanced Book Classics. Boulder, Colo.: Westview Press, 1991.

Munkres has managed to write one of the best introductions to analysis on manifolds and differential forms available. The exposition is clear, rigorous and very detailed. In fact, the level of detail in parts of the book borders on the excessive side as many readers will find essential aspects of the theory are hidden by the mass of minutia. The algebraic topology book by the same author suffers from the same problem. The exercises are plentiful and well motivated, and range from very easy to very difficult. The treatment of differential forms is motivated more naturally than in any other text I have found. The organization of the book is masterful, and the selection of topics is also a work of art. Watch out for shoddy bindings on this text as I have yet to find a used copy with an intact spine.

Aliprantis, Charalambos D., and Owen Burkinshaw. Principles of Real Analysis. 3rd ed. San Diego: Academic Press, 1998.

Aliprantis, Charalambos D., Owen Burkinshaw, and Charalambos D. Aliprantis. Problems in Real Analysis: A Workbook with Solutions. 2nd ed. San Diego: Academic Press, 1999.

This book is an easy to read introduction to real analysis that is accessible to beginning graduate students and advanced undergraduates. Several more advanced topics are scattered throughout the text. The text is not appropriate for a PhD level class in real analysis. The exercises are well thought out and support the material very well. One of the best features of this book, and why I highly recommend it, is the companion volume by the same authors. This companion volume has every exercise in this text worked out in great detail. The combination of both books makes an excellent choice for independent study.

Ahlfors, Lars V. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable. 3d ed. International Series in Pure and Applied Mathematics. New York: McGraw-Hill, 1979.

This is a fantastic book. The exposition is well organized, rigorous, and lucid. The exercises are thoughtful and appropriate. The selection of topics is typical of a first or second year introduction to complex analysis. The level is best suited for readers with some background in mathematics. This is absolutely a "must read" for anyone interested in a thorough understanding of basic complex analysis. BTW, this book tends to be quite expensive.

Hille, Einar. Analytic Function Theory V1. Place of publication not identified: American Mathematical Soc, 2012.

Hille, Einar and American Mathematical Society. Analytic Function Theory V2. Providence: AMS Chelsea Publishing, 2002.

This is a classic text covering a classical topic. If you are lucky enough to find this old text, then buy it for your library! The coverage is excellent, the exposition is clear and precise, the exercises are great, and the attention to detail is refreshing. The level of mathematical maturity required to read this book is a bit higher than a typical introduction to complex analysis.

Rudin, Walter. Functional Analysis. 2nd ed. International Series in Pure and Applied Mathematics. New York: McGraw-Hill, 1991.

This classic text is the most readable book I have found covering functional analysis. The author presents the material in a very well organized way that is clear, precise, and rigorous. The exercises are interesting, thoughtful, and sometimes quite difficult. This book could easily serve as the basis for a one or two semester class on functional analysis following a standard PhD level real analysis class covering Lebesgue integration. It is important to realize that the mathematical prerequisites for this book are a good understanding of Lebesgue measure and integration. This text is quite suitable for self study.

Logan, J. David. A First Course in Differential Equations. 2nd ed. Undergraduate Texts in Mathematics. New York: Springer, 2011.

Most ODE books are simply too long, and many first, undergraduate texts resemble garishly illustrated catalogs of computational techniques. This little book is less than 300 pages, and still manages to cover all the most important topics well. The exercises and examples are interesting, and reinforce the material well. Overall, this is probably the best "short" introduction to ODEs I have found – similar to the same author's PDE book

Logan, J. David. Applied Partial Differential Equations. 3rd ed. Undergraduate Texts in Mathematics. Cham Heidelberg New York Dordrecht London: Springer, 2015.

This slim little book is a fantastic introduction to PDEs that manages to cover all of the essentials in about 200 pages. The writing is clear and easy to understand even for the less mathematically prepared reader. The exercises and examples are interesting, and reinforce the material well. The exercises could be more challenging. Overall, this is probably the best "short" introduction to PDEs I have found – similar to the same author's ODE book.

Jordan, D. W., and Peter Smith. Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers. 4th ed. Oxford [England]: New York : Oxford University Press, 2007.

Through a great many richly illustrated and well motivated examples, this text demonstrates the essential techniques of qualitative analysis that are so important in understanding the solutions of real world ODEs. This work can provide an answer to the dearth of coverage of qualitative techniques normally found in most ODE texts. While the exposition is clear, the text contains numerous typos, and can be a bit terse – less prepared readers will stumble a bit when trying to fill in the blanks. An enormous number of exercises are included, and provide a range of difficulty for the reader.

Hairer, E., S. P. Nørsett, and Gerhard Wanner. Solving Ordinary Differential Equations I: Nonstiff Problems. 2nd ed. Springer Series in Computational Mathematics 8. Heidelberg ; London: Springer, 2009.

Hairer, E., S. P. Nørsett, and Gerhard Wanner. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. 2nd ed. Springer Series in Computational Mathematics 8, 14. Berlin ; New York: Springer-Verlag, 1993.

Hairer, E., Christian Lubich, and Gerhard Wanner. Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations. 2nd ed. Springer Series in Computational Mathematics 31. Berlin ; New York: Springer, 2006.

These three books are amazing. Hands down the best coverage of modern numerical techniques for solving ODEs. The code in the books is solid, and available online. You don't need to buy anything else. This is it.

Holmes, Mark H. Introduction to Numerical Methods in Differential Equations. Texts in Applied Mathematics 52. New York: Springer, 2007.

If you are looking for a quick read so you can get a feel for how to solve ODEs numerically, then this is an excellent introduction to the subject. See Hairer et al for more comprehensive coverage.

Higham, Nicholas J. Accuracy and Stability of Numerical Algorithms. 2nd ed. Philadelphia: Society for Industrial and Applied Mathematics, 2002.

This is not a general numerical analysis text, but a deep and detailed treatment of the accuracy and stability for numerical algorithms. While some of the material concerns these topics in general, most of the text centers around the techniques and algorithms of numerical linear algebra. The text is more than readable, but it requires quite a lot of mathematical sophistication on the part of the reader. The presentation is very careful and rigorous. This is a scholarly work that is well annotated, and is worth the price for the bibliographic material and reference notes alone. The exercise sets and examples are unusually well thought out. One of my favorite books

Tyrtyshnikov, E. E. A Brief Introduction to Numerical Analysis. New York: Springer Science+Business Media, 1997.

This is a wonderful book! This book won't give you what you need to become a numerical analyst; however, it is one of the best ways to get quickly acquainted with modern numerical analysis or if you need a refresher. This book is full of stuff that I wish I had known when I took my first numerical class. The writing is terse but clear. The organization is well thought out.

Muller, J. M. Elementary Functions: Algorithms and Implementation. 3rd ed. Boston: Birkhäuser, 2016.

This is the de-facto standard work when it comes to implementing and understanding software for the computation of elementary functions like sin, cos, and log. All of the most important techniques used in the computation of such functions are covered at great depth and with extreme care. The successful reader should be well prepared to implement real software not only for the elementary functions directly discussed in the text but a great many other functions as well as the techniques are broadly applicable. The analysis of error bounds and edge conditions is extraordinary. The exercises are sparse, but well thought out and interesting. The book is loaded with fantastic and well constructed examples. If you need to accurately approximate a function, then this is the one book to have on your shelf. If you are interested in the error analysis of numerical algorithms, then this book should be on your shelf. While the topic may be considered esoteric in this day and age, this work is one of my favorite numerical analysis texts.

Quarteroni, Alfio, Riccardo Sacco, and Fausto Saleri. Numerical Mathematics. 2nd ed. Texts in Applied Mathematics 37. Berlin ; New York: Springer, 2007.

This book is a comprehensive introduction to numerical analysis that includes many topics frequently missing from introductory texts. The selection of topics is complete, the exposition is clear, the proofs well constructed, and the exercises well thought out. That said, the prose is a bit terse in places, and can sometimes be a bit less precise than I would prefer. This can be a very difficult book for beginners or readers with insufficient mathematical preparation. After reading this book, the reader is capable of implementing real software and understanding how it works. Unlike most numerical analysis books, this one uses MATLAB for example implementations and experiments – I think this is actually a disadvantage. The code is highly reliable.

Watkins, David S. Fundamentals of Matrix Computations. 3rd ed. Pure and Applied Mathematics. Hoboken, N.J: Wiley, 2010.

This is one of the best books on numerical linear algebra available today. The second edition is an updated and slightly expanded version of the first. Like the first edition, this one is well organized, easy to read, and full of good exercises. Like the first edition, this book makes for a fine text for an undergraduate class in numerical linear algebra – in fact, it is far less difficult for undergraduates than many of the alternative texts. While the first edition could have been successfully used as a graduate text, this second edition is far more suitable for graduate use. In particular, several more advanced topics have been scattered throughout the book, the organization has been changed, and a new chapter on iterative methods has been added. Many of the exercises are embedded in the text, and core material is often only presented in such exercises. This leaves some details to the reader who must be willing to stop and work through them for maximal value. The book has no source code, but is full of pseudo code. This new edition has the original Fortran exercises, which I think is essential even in this modern era; however, it is also full of new Matlab exercises and examples.

Saad, Y. Iterative Methods for Sparse Linear Systems. 2nd ed. Philadelphia: SIAM, 2003.

This is the definitive work on iterative systems from one of the pioneers in the field. It is uncommon to find experts that are able to communicate so clearly. This book is easy to read, and is appropriate for reference, self study, or as a text. The organization is well done. The exercises are well thought out. If you need to know about iterative methods for linear systems, then this is the book to own.

Golub, Gene H., and Charles F. Van Loan. Matrix Computations. 4th ed. Johns Hopkins Studies in the Mathematical Sciences. Baltimore: The Johns Hopkins University Press, 2013.

One of the best collections of facts about numerical linear algebra algorithms to be found today. The presentation is more practical than rigorous, and the coverage is encyclopedic but somewhat terse. This is not a book from which to learn the material for the first time unless one has a very high level of mathematical maturity. A few mistakes are peppered throughout, but they are all well known and documented in the errata sheet. This work is valuable for both people developing code and people trying to make intelligent use of existing software. In short, this is a must own reference book for the desk of a practicing numerical analyst or scientist.

Trefethen, Lloyd N., and David Bau. Numerical Linear Algebra. Philadelphia: Society for Industrial and Applied Mathematics, 1997.

The unorthodox organization of this numerical linear algebra text makes it one of the most valuable introductory books in the field. The reader is likely to obtain a better intuitive understanding of topics like the SVD and the intimate relationship it has with linear transformations, eigen structure, and stability. The book is for the beginner, but a good background in basic linear algebra and calculus is required. The writing is clear and direct, but can be a terse in places. While the presentation is mostly rigorous, it may leave more experienced readers wanting more. The examples and exercises are interesting and reinforce the material; however, I would have preferred more, and meatier, exercises. While it can't stand alone as the only numerical linear algebra book the well rounded practitioner needs, it definitely should be in every applied mathematician's library.

Varga, Richard S. Matrix Iterative Analysis. 2nd ed. Springer Series in Computational Mathematics 27. Berlin ; New York: Springer Verlag, 2000.

This little book is truly a classic. It is easy to understand and well organized. This is not the book to read for a modern perspective; however, it provides a wonderful glimpse into the historical development of matrix iterative methods. For a more modern and complete treatment, consider the book by Yousef Saad.

Varga, Richard S. Geršgorin and His Circles. Springer Series in Computational Mathematics 36. Berlin; New York: Springer, 2004.

This is a lovely little book on a lovey topic. Very highly recommended.

Dennis, J. E., and Robert B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Classics in Applied Mathematics 16. Philadelphia: Society for Industrial and Applied Mathematics, 1996.

This is a fabulous book is a pleasure to read. It is a bit long in the tooth; however, the methods and techniques are still valuable and widely used today. The organization and writing are both first rate. Good advice as well as clear mathematics are found throughout. This book would make welcome supplemental reading for a first graduate class in optimization.

Baldick, Ross. Applied Optimization: Formulation and Algorithms for Engineering Systems. Cambridge: Cambridge University Press, 2009.

This is a delightful book aimed at the non-specialist user of optimization software. The selection of topics is appropriate, and wide enough to provide the novice reader with a broad understanding of the field. It is just deep enough so that the reader is able to understand how to effectively select and use existing software, but not so deep that a reader could implement good optimization software. While I can not recommend this work for specialists or even perhaps for mathematicians, I can whole heartily suggest this text for the novice to optimization or to the non-specialist practitioner. In fact, for the non-specialist practitioner, this may be one of the best books available today.

Gentle, James E. Random Number Generation and Monte Carlo Methods. 2nd ed. New York, NY: Springer, 2006.

Gentle's book is a comprehensive and modern overview of random number generation techniques. Most of the important generators are covered in detail – algorithms, quality measures, and use patterns. The writing is clear, and the exercises are well motivated. The bibliography is extensive, and worth the price of the book by itself.

Wilcox, Rand R. Fundamentals of Modern Statistical Methods: Substantially Improving Power and Accuracy. 2nd ed. New York, NY: Springer, 2010.

This book provides a whirlwind tour of the fundamental problems inherent in traditional statistical methods and some modern alternatives to get around them. This work is not mathematically deep or very precise, but it is a wonderful introduction to the subject. This is the book that I recommend to most people who need a basic understanding of why the statistics they had to learn in school simply don't work.

Ziliak, Stephen Thomas, and Deirdre N. McCloskey. The Cult of Statistical Significance: How the Standard Error Costs Us Jobs, Justice, and Lives. Economics, Cognition, and Society. Ann Arbor: University of Michigan Press, 2008.

There are many books discussing common errors in the application of statistics. This book is not in the same category. Rather, this work brilliantly exposes the truly astounding way that statistical significance techniques have been recast into check-box driven tools of misinformation that are perpetuated by poorly designed statistical education and the ever growing scientific bureaucracy.

The book is able to illustrate the institutionalization of poor statistical methods in a truly disturbing number scientific fields of study ranging from management science (MBA's take note) to physics. The authors clearly show that by transforming statistical significance techniques into what amounts to little more than the practice of a mathematical ritual to the Gods of probability, the power and value of the technique is completely lost. An incredible number of wide reaching and serious consequences of the resulting poor decisions are beautifully illustrated in the book.

The book has some flaws. The most obvious is that the authors provide little aid for the non-statistician wishing to keep from falling into the very statistical trap they so carefully expose. My remaining complaints are simply a matter of style. As a more mathematically inclined reader, I would have preferred a more concise exposition; however, I expect that the non-specialist might prefer the more story based, rather combative, approach taken.

This work should be required reading for everyone wishing to make use of statistics in the real world.

Brockwell, Peter J., and Richard A. Davis. Time Series: Theory and Methods. 2. ed., Reprint of the 1991 ed. Springer Series in Statistics. New York, NY: Springer, 2006.

This is one of the best introductions to time series that can be found today. The writing is clear, the coverage of the topic is comprehensive, and the mathematical treatment is precise. The level of sophistication required from the reader is that of a graduate student in statistics or mathematics. This is the one book to own on this topic.

McCullagh, P, and J. A Nelder. Generalized Linear Models. Boca Raton: Routledge, 2018.

This is a classic, and authoritative, text on the subject of GLM – a must have for the shelf of any practicing statistician. The work is well organized, and clearly written. The coverage is comprehensive, deep, and carefully rigorous.

Loader, Clive. Local Regression and Likelihood. Statistics and Computing. New York: Springer, 1999.

This book is a wonderful introduction to the field of local regression. It is very clearly written and quite an easy read. This book is worth it's price just for the historical introduction in the first chapter. Extensive coverage is provided of the author's R package for local regression LOCFIT).

Platt, Charles. Make: Electronics. 2nd ed. San Francisco, CA: MakerMedia, 2015.

A fun, very basic introduction to electronics.

Scherz, Paul, and Simon Monk. Practical Electronics for Inventors. Third edition. New York: McGraw-Hill, 2013.

An excellent introduction to practical electronics and electromechanical devices.

Horowitz, Paul. The Art of Electronics. Third edition. New York, NY: Cambridge University Press, 2015.

Horowitz, Paul, Winfield Hill, and Paul Horowitz. The Art of Electronics: The x-Chapters. Cambridge ; New York, NY: Cambridge University Press, 2020.

One of my favorite electronics books. It's a bit dated at this point, but it's still a good read.

Platt, C. Encyclopedia of Electronic Components V1. O’Reilly Media, 2012

Platt, C., and F. Jansson. Encyclopedia of Electronic Components V2. Make Community, LLC, 2014

These are great books for the hobbyist wishing to learn a bit more about electronic components.

Glisson, Tildon H. Introduction to Circuit Analysis and Design. Dordrecht: Springer Netherlands, 2011

This text covers the typical topics for the standard first circuits course most EEs take. The author takes an extraordinarily careful and deliberate path through the material providing clear explanations, good examples, and a great number of exercises. Because of the careful sequencing of topics the text is a bit of a longer read than some of the alternatives, and it can seem a bit wordy. Frankly both of these items are features when it comes to using the text for self study. That said, this is not a work for the impatient reader – for that See Prasad's book listed below.

May, Colin. Passive Circuit Analysis with LTspice: An Interactive Approach. Cham: Springer International Publishing, 2020

In my opinion combining circuit simulation software with that first circuits book is very valuable. When doing all those exercises by hand, redo them with the aid of a simulator. When reading about a new kind of circuit, simulate it and variations to see how it behaves. This text is one of the best works I have found to act as a simulator companion for that first circuits book. It is also a great way to learn about LTSpice.

Gift, Stephan J. G., and Brent Maundy. Electronic Circuit Design and Application. Cham: Springer International Publishing, 2021

And this one covers the material from that typical second class in circuits.

Prasad, R. Analog and Digital Electronic Circuits: Fundamentals, Analysis, and Applications. Undergraduate Lecture Notes in Physics. Cham: Springer International Publishing, 2021

This text is an odd duck. First it is an introductory text; however, it pulls no punches and requires a solid background. For example I think readers with a good understanding of circuits from an Engineering physics course would be fine. This book is also odd in that it covers most of the topics from the topics of typical "circuits" and "circuits & devices" courses – and some from an introduction to digital electronics too – even at almost 1000 pages it must be concise to cover so much ground. This makes it a great reference. It also makes it a great book for those self-taught hobbyists who are approaching the subject with a lot of knowledge, but a few holes they wish to fill. Another odd thing, one I applaud, is the introduction of the Laplace transform sooner rather than later. Overall this is a great book. Be aware of some typos and occasionally English prose that is clear, but less than elegant.

Dimopoulos, Hercules G. Analog Electronic Filters. Dordrecht: Springer Netherlands, 2012

A comprehensive, clearly written, and modern treatment of the subject. My favorite filter book.

Su, Kendall. Analog Filters, 2002.

While a bit dated this is still a great work on passive filters. It's a bit skimpy on active filters, and some practical aspects of real world components. Th book is concise and the exposition is very clear. The included MATLAB code is very handy.

Huijsing, Johan. Operational Amplifiers. Cham: Springer International Publishing, 2017

This isn't a book about using opamps, but about designing them. That might not sound useful for someone wishing to simply make use of opamps, but understanding how they work is a tremendously powerful tool in understanding how to make use of them. Not a book for beginners. Highly recommended.

Carter, Bruce, Ron Mancini, and an O’Reilly Media Company Safari. Op Amps for Everyone. 5th ed., 2017

I often recommend this book to people just starting out with operational amplifiers. It's practical, clear, and pretty easy to understand.

Buscarino, Arturo, Luigi Fortuna, Mattia Frasca, and Gregorio Sciuto. A Concise Guide to Chaotic Electronic Circuits. SpringerBriefs in Applied Sciences and Technology. Cham: Springer International Publishing, 2014.

This is a great, compact guide to the the most common chaotic circuits. Enough detail is provided to actually build and analyze the circuits in the lab. This is a fun little book. Highly recommended.

Muthuswamy, Bharathwaj, and Santo Banerjee. Introduction to Nonlinear Circuits and Networks. Cham: Springer International Publishing, 2019.

A readable introduction to non-linear circuits and chaos. A very practical emphasis on circuit simulation with QUCS.

Fortuna, L., Mattia Frasca, and Maria Gabriella Xibilia. Chua's Circuit Implementations: Yesterday, Today, and Tomorrow. World Scientific Series on Nonlinear Science, Series A. Singapore ; Hackensack, N.J: World Scientific Pub, 2009.

With over two hundred pages devoted to nothing but Chua's Circuit, this is one of the most comprehensive overviews available.

Sprott, Julien C. Elegant Chaos: Algebraically Simple Chaotic Flows. New Jersey: World Scientific, 2010.

Most of this work is devoted to the theoretical; however, the final chapter is devoted to chaotic circuits.

Sprott, Julien Clinton, and Wesley Joo-Chen Thio. Elegant Circuits: Simple Chaotic Oscillators. New Jersey: World Scientific, 2022.

A wonderful tour of dozens of different chaotic circuits – each with a discussion of the governing equations, simulation results, physical measurements, and circuit schematics.

Brauer, Fred, Carlos Castillo-Chavez, and Zhilan Feng. Mathematical Models in Epidemiology. Vol. 69. Texts in Applied Mathematics. New York, NY: Springer New York, 2019

Probably the best elementary introduction to the topic I have found, and the one I generally recommend to non-mathematicians wishing to learn more.

Martcheva, Maia. An Introduction to Mathematical Epidemiology. Vol. 61. Texts in Applied Mathematics. Boston, MA: Springer US, 2015

A nice introduction to the subject. Less expensive than the Brauer.

Bjørnstad, Ottar N. Epidemics: Models and Data Using R. Use R! Cham: Springer International Publishing, 2018

If you are an R nut, and want some practical examples of how to fit models then this is a fun book. It is not an introduction

Yan, Ping, and Gerardo Chowell. Quantitative Methods for Investigating Infectious Disease Outbreaks. Vol. 70. Texts in Applied Mathematics. Cham: Springer International Publishing, 2019

If you have a bent for the statistical/probabilistic side, then this is a neat book. They do a good job of connecting life/hazard probability to the DEQ systems within the models. Read this one after you read Brauer or Martcheva.

Jennings, D. H., and G. Lysek. Fungal Biology: Understanding the Fungal Lifestyle. 2nd ed. Oxford, UK : New York, NY: BIOS ; Springer, 1999.

This fantastic little book requires a bit of biological knowledge to be fully appreciated, but it is reasonably readable for even the layperson. While a bit slim to serve as the primary textbook for an introductory mycology course, this work should surely be on the supplemental reading list for any such course. The bibliography is not extensive; however, it is densely stocked with some of the highest quality sources available today. This is absolutely my favorite mycology book.

Delbeek, J. Charles, and Julian Sprung. The Reef Aquarium V1: A Comprehensive Guide to the Identification and Care of Tropical Marine Invertebrates. 1st ed. Coconut Grove, Fla: Ricordea Pub, 1994.

Delbeek, J. Charles, and Julian Sprung. The Reef Aquarium V2: A Comprehensive Guide to the Identification and Care of Tropical Marine Invertebrates. Coconut Grove, Fla.: Ricordea Pub., 1994.

Delbeek, J. Charles, and Julian Sprung. The Reef Aquarium V3: Science, Art, and Technology. Coconut Grove, Fla.: Ricordea Pub., 1994.

This collection is the bible for reef aquarium keepers world wide. This volume dives deeply into the science of reef aquarium, but it also provides substantial practical information about things like support equipment operation and selection. Finally this volume also provides extensive coverage of the more delicate aspects of system design including the aesthetic aspects, ease of upkeep, fitting an aquarium into your home (aesthetic and the plumbing too), and much more. I can not recommend this book, the entire set in fact, too highly - both for aquarium keepers and anyone interested in reef biology.