The Ultimate Crash Course for STEM Majors — What’s Inside and Which Edition to Choose

Based on the supplied transcript. Punctuation and paragraph breaks have been added, with repeated fillers and false starts reduced for readability. Obvious transcription errors have been corrected. The speaker’s opinions and descriptions of the products are retained.

Hi, kids. This is a discussion about my Ultimate Crash Course, the original book I wrote, why I wrote it, and what it is good for—for you.

First of all, I’ve tossed these things around. They’re pretty well built, actually. I get angry, and I’m like, “Ah!” They’re old.

This particular book, The Ultimate Crash Course for STEM Majors, has The Ultimate Cheat Sheet in it. It’s thicker than just the individual books. It has both The Ultimate Cheat Sheet and The Ultimate Crash Course.

I’m going to do a screen recording next and show you. What The Ultimate Crash Course is: when students are in calculus, out of calculus, or preparing for calculus, 50% are guaranteed to fail across the board. That usually has everything to do with their ability to do algebraic arithmetic.

You understand the question. Calculus is easy: solve the integral. You’re like, “Okay, I know how to do that.” But then you can’t do the arithmetic, or you botch it.

The first thing I do is show you the algebra most important for calculus: the algebraic arithmetic and the notation you misunderstand.

There isn’t much trigonometry in there because, through calculus, it’s sine, cosine, cosine, sine, 3.14159. There isn’t much trigonometry compared with the trigonometry course. It’s relatively basic.

I took James Stewart’s Calculus textbook and went through every section, all the way through sequences and series. That includes differential and integral calculus, parametric equations, polar equations, and so on.

For every section, I created a detailed lesson. I wrote it from your point of view on purpose. It reads like the notes of a college student who knows what they’re doing.

The math journal is written very professionally. This book is written from your point of view because you need a more keen eye to read something like the journal. That’s why I wrote it this way.

If a PhD looked at it, they might say, “What is this?” I’d say, “It’s a book for somebody who has never taken calculus and doesn’t understand anything.” Then they’d say, “Okay, that makes sense.”

I wrote it live. About 600 or 700 videos of me recording myself writing it come with the purchase of the Triple Play.

If you get the hardcover, it won’t automatically include website access. But if you show me your receipt, I’ll give you access. Send me the receipt, and I’ll send you the information to download the PDFs and access the videos.

That’s if you prefer a hardcover. Most people, ten to one, prefer the PDFs. It’s the digital age. It makes no sense to have a physical book. The physical books are like a novelty—a novelty novel—but they’re there if you want one.

I recommend the Triple Play bundle. You get all my books, including my fiction, which I’ve given up on. I don’t want to do fiction anymore. Dealing with reviews is too stressful. I can’t handle it. It isn’t for me. I like math and physics.

You’ll get access to the fiction. Don’t judge me when you read it. It’s fiction. I wrote it to piss people off on purpose because I know my neighbors and knew they—but anyway.

The purpose of the book: I wrote it from your point of view and went through Stewart’s Calculus, which is almost essentially identical to Thomas’ Calculus. It essentially covers the questions in calculus courses through sequences and series.

In the integration material, there are also more than 100 additional integrals.

Listen carefully: I took the trick questions students mess up on. I spent 15 years tutoring, and the questions you repeatedly struggled with are what I put in the book.

It’s organized from start to finish in the same order as the James Stewart and Thomas calculus books.

Then I introduce vector calculus because, if you need help after Calculus One and Two, you’re in the wrong field. If you’re in math, physics, or engineering and need assistance after Calculus Two, you need to change your major.

If you aren’t in math, physics, or engineering and just have to take that course, who cares? Do what you have to do.

I also introduce linear algebra and advanced notation to prepare you for junior- and senior-level engineering topics, including tensor analysis, index notation, and differential equations.

Then I show a little proof material, such as number theory proofs and other things. After 15 years of tutoring, I isolated the things students have problems with.

My message is: if you need help after that book, you’re in the wrong major. That’s it.

Many people have come back and said, “This book saved my life.” Others have said the same thing in the opposite direction: “You were right. I needed to change my major,” or, “I needed to change how I study.” That’s the consensus.

The Ultimate Crash Course is half of this book, and The Ultimate Cheat Sheet is the other half.

I also have Quartic Play. Let me show you that one. This is a big book. It contains about 200 podcast summaries, plus the physics book.

The popular How I Study book isn’t in that section; it’s in The Ultimate Cheat Sheet.

If you want a hardcover, Quartic Play includes everything. If you’re a STEM major, I would choose that. If you’re a PLEM major—math, physics, or engineering—I’d get the Red Edition.

The Red Edition doesn’t have the podcast summaries. It has this additional book: about 200 extra pages of professionally written, full-circle mathematics solutions.

They cover a wide variety of advanced and basic math. We did proofs involving Maxwell’s equations, basic algebra with an advanced eye, physics questions, relativistic physics, and other topics.

It shows what you should be doing by junior year. That book demonstrates how you should be operating by junior year if you’re a PLEM major.

If you don’t have to go beyond calculus or you aren’t in math, physics, or engineering, Quartic Play is the book you’d want. If you are a math, physics, or engineering student, you’d want the Red Edition.

That’s how my crash course books work. The description has hardcover purchase links and PDF bundle links.

All purchases come with a library. There are about 250 older podcasts of me with long hair, beating you up a little and making you laugh.

You’ll get my fiction and audiobooks. I’m uploading the audiobooks at some point. There are also about 600 or 700 videos of me writing the book.

Once you watch about ten, you probably won’t need to watch more because you’ll understand what I’m telling you.

I’m going in a different direction now to help people prepare for employment. That earlier work was to help repair the damage done freshman and sophomore year by things like Khan Academy, AI, Wyzant tutoring, and pirated solution manuals.

It’s meant to repair the damage from an incorrect way of thinking.

Check it out. It’s $99 for the PDF package, and you get about 1,000 videos. That’s a pretty good deal. You also get my fiction, which is worth something.

That’s that. I’ll show you a preview of the inside of the book next. Have a nice day. Check it out.

Professor Jonathan D. Tullis explains the purpose, organization, and available editions of his crash course collection. He describes developing the material around difficulties he repeatedly observed during approximately 15 years of tutoring.

Algebraic Preparation for Calculus

The opening material focuses on algebraic manipulation and notation used in calculus. Professor Tullis emphasizes situations in which a student recognizes the calculus method but makes mistakes in the algebra needed to complete the calculation.

Detailed Calculus Lessons

The crash course is described as following the progression of James Stewart’s calculus text through sequences and series, with differential calculus, integral calculus, parametric equations, and polar equations. Additional integration examples focus on questions students commonly find troublesome.

Written from the Student’s Perspective

Professor Tullis describes the presentation as resembling detailed notes from a student who understands the material. He contrasts this accessible style with the more formal mathematical writing used in the journal and advanced solutions.

Introductions to Later Topics

The collection also introduces vector calculus, linear algebra, differential equations, index notation, tensor-related topics, and selected proofs. These introductions are intended to help readers recognize the transition toward more advanced coursework.

Which Hardcover Does He Recommend?

PDFs & Accompanying Lessons

Professor Tullis recommends the Triple Play PDF bundle for readers who prefer digital access. He describes an accompanying collection of lesson recordings and podcasts, including videos of the book being written. Hardcover purchasers are instructed to send their purchase receipt to receive access information.

Edition contents, approximate recording counts, and the price mentioned in the transcript reflect the speaker’s description at the time of recording. Consult the linked product pages for the offer you intend to purchase.