I’m happy to announce the No Bullshit Guide to Math & Physics version 5.4 has been released. This update contains two years’ worth of text improvements based on readers’ feedback and suggestions. The main focus of the edits was the math fundamentals chapter, making it easier to follow for beginners. The other big news is that the book is now available in .epub and .mobi formats.
In this blog post I’ll give an overview of the changes to the book with additional comments about the importance of each change. I’ve included links to PDF excerpts of all the new sections[1,2,3,4,5,6] as well as a detailed red-blue diff that shows all edits. All this with the goal to make the PDFs linked to from this blog post to contain a the complete “patch” information for readers who have an older version of the book.
New .epub and .mobi formats
The book is now available as .epub and .mobi files. Making the book available in a “reflowable” format that works on all devices (mobile and eReaders) is something that I’ve been promising readers for a very long time. I’m very happy to finally be able to keep this promise after all these years.
Generating decent-looking ePub and Mobi files from LaTeX source full of math equations wasn’t easy, but after many coffees and late nights I managed to build a pipeline based on TexSoup, Softcover, and Calibre that works great. See this tech blog post for details about this new eBook generation pipeline.
Summary of changes in v5.3 → v5.4
The high school math chapter received some much-needed revisions to smooth over several parts that were not explained well:
- Functions: I improved the explanations of functions’ input and output sets and their properties (injective, surjective, bijective). Several readers said their eyes “glazed over” when they were reading these parts of the book, so I knew I had to “reinforce” that section by giving precise definitions, adding figures, examples, and explanations about why this fancy-sounding terminology is worth learning.
- Polar coordinates: The section on circles was greatly expanded to properly explain the polar coordinate system: what is it, why is it important, and how we can use it to represent points, equations, and functions. Previously the concept of polar coordinates was just dropped in readers’ lap without any context or pictures. I’ve fixed that now with nice explanations of polar coordinates $r\angle \theta$ and their use for representing equations and functions.
- Parabola: I added this section so the book now has a complete coverage of all four conic sections: circle, ellipse, parabola, and hyperbola.
- Completing the square: I added a much needed illustration of this important algebra procedure. Many people advised me to remove this section since it requires too much “math suffering” to understand. I listened to this feedback, but wasn’t having any of it. Understanding this algebra trick and the geometric intuition behind it (Figure 1.15) is an essential “checkpoint” on every reader’s journey toward math proficiency. I owe it to my readers to bring them over this hump, and show them that algebra is not something to be afraid of, but a toolbox of very useful tricks. In other words, this is necessary math suffering and y’all need to know this!
- Linear equations: I added several figures (Figure 1.77, Figure 1.78) to illustrate the connection between the algebraic and geometric representations of linear equations. The algebraic equation $ax+by=c$ corresponds to a line in the Cartesian plane—the line consisting of all the coordinate pairs $(x,y)$ that satisfy this equation. Understanding this geometric interpretation of linear equations gives us another way to find solutions for systems of linear equations: the solution to a system of equations consisting of two lines is where the lines meet (Figure 1.79, Figure 1.80, desmos:exikik615f). The geometry connection is useful for describing the special cases of no solutions when the lines are parallel (Figure 1.82) and infinite number of solutions when the lines overlap (Figure 1.83).
- Vectors: I added some explanations about the algebra rules for equations that combine points and vectors. I also added an example that motivates the importance of knowing the coordinate systems used to represent vectors.
- Notation: I stopped using the symbol ≡ (\equiv) which was confusing for many readers, and instead prefer the regular equality sign (=) and occasional use of the symbol ≝ in definitions.
- Errata: I fixed errors in the solutions to problems P4.40 and P4.41. See the errata file for details. When a book contains hundreds of solved problems, it’s inevitable that some errors with slip in. Thanks to feedback from serious readers that solve all the problems in the book, I have been fixing these errors. I can now assert that the solutions to the exercise and problems in the book have been fact-checked by numerous students, technology professionals, and homeschooling moms. There are probably still some errors left, but very few.
Most of these fixes and clarifications are the result of comments and questions I’ve received from readers. Having an open communication channel with readers (email: firstname.lastname@example.org) has been tremendously useful since they tell me which parts of the book are confusing and in need of further clarifications. If there’s anything I’ve learned about startups over the years, it’s that listening to the users is a good thing.
The recent work on a French translation of the book was another source of feedback and improvements. Working closely with the translator (a math professor) was an amazing experience, as he “called bullshit” on several missing definitions, imprecise analogies, and hand-wavy explanations. I didn’t expect this, but it turns out the translation process is an excellent “test” for explanations: if an explanation is not 100% clear it won’t translate well. All “weak spots” in the original get magnified by the translation process and it makes it easy to spot the places in the original that need more work. I wrote a blog post about this “authoring hack” and others, see Multilingual authoring for the win.
For a detailed red-blue diff of all the changes between v5.3 and v5.4, see this file diff_noBSmathphys_v53_v54.pdf (250 pages). The text shown in red has been removed, while the text shown in blue has been added. (Tech sidenote: this word-level diff was generated using latexdiff, which is an amazing tool that I recommend for anyone writing in LaTeX. More generally, anyone using git for text files can use the command
git diff --color-words to get a similar word-level diff instead of the default line-level diff.)
New point system for progress tracking
Many readers of the book are adult learners interested in (re)learning math and physics for personal interest and not students studying for a specific course or exam. I’ve been asked repeatedly to create an accompanying online course to provide some structure and accountability for independent learners’ journeys through the book. The book covers the material from three university-level courses, so it’s understandable that an external support structure would be useful!
I’m working on video tutorials, an offline self-directed course pack, email lessons, and maybe even a mobile app of some sort, but these projects will take time to research, develop, and ship. Rest assured the query
SELECT * FROM EdTech WHERE license="free" AND good=TRUE; is continuously running and there are some really good matches you’ll be hearing about soon[K,M]. Expect good things in 2021. In the meantime, I have a “hack” for you that provides some of the benefits of an online course.
Gamify-it-yourself: There are 500 pages to read in the book, organized into five chapters, and each chapter is like a stage in a computer game. The concept maps in the front of the book show the concepts and topics you need to learn to complete each stage. Print the concept maps and post them somewhere visible. Use a pen or pencil (old-school EdTech) to represent your current state of knowledge about each term in the concept map using the following criteria:
Add a single dot (●) next to all concepts you’ve heard of, two dots (●●) next to concepts you think you know, and three dots (●●●) next to concepts you’ve used in exercises and problems.
Basically, you can gamify your learning process using a piece of paper and some metacognitive skills. Who better to reward your curiosity, learning, and practice than yourself? Trust me, there is no intelligent tutoring system or machine learning model out there that is anywhere close to what you can do.
The goal of the dot system is to give partial credit for all types of learning: heard about concept X, understood concept X, and know how to apply concept X. To get all the points you must not only read about and understand the concepts from all five chapters, but also practiced using these concepts. It might take a month or two, but at any point in the “game” you can check your learner profile and know what is coming next, and how much is left.
If you purchased the book from gumroad, use the link you received by email to access the latest files. If you have a print copy of the book, you can send me a proof of purchase (e.g. picture or receipt email) to email@example.com and I’ll send you the the latest eBooks. There is probably no point in purchasing a new print copy for yourself, but you should consider buying a copy for a friend or family member who might benefit from having some math and physics in their life (holidays coming up).
New readers can get the book in print or digital form from the following links:
- Softcover print from lulu: bit.ly/noBSmathphys-sc (this is the original softcover version for US$39).
- Hardcover print from lulu: bit.ly/noBSmathphys-hc (this is a “deluxe” version of the book for US$59 you should get this one if money is not an issue).
- Softcover from amazon: amzn.com/0992001005 (similar to the lulu softcover but sold by amazon so they sometimes have price discounts and offer free shipping).
- Digital download from gumroad: gum.co/noBSmathphys (get the eBook for US$29 if you don’t want to carry a physical book around).
The No Bullshit Guide to Math & Physics is the ideal book for last-year high school students, first-year university students, and adult learners who want to learn calculus and mechanics. The book explains all the material required for first year science courses in an easy to understand, conversational tone. Don’t take my word for it though, check the amazon reviews to see what other readers have said, and check out the extended preview and sample chapter (170 pages) to see for yourself.
Note: if you’re interested in (re)learning high school math topics, but don’t want to go all the way to mechanics and calculus, then you should get the No Bullshit Guide to Mathematics (print or digital), which covers only the essential math fundamentals (Chapter 1 and Chapter 3 of the Math & Physics book). The green book is great for high school students and parents of such.