How to Learn from a Textbook in College — Reading, Notes & Practice

Math Monthly — How to Study

How to Learn from a Textbook in College — Reading, Notes & Practice

Author Jonathan David explains his approach to preparing for mathematics and physics courses: begin reading ahead, organize definitions and formulas, study the text carefully, and practice worked examples until you can reproduce the reasoning independently.

Watch this textbook study discussion on YouTube ↗

The Study Process Discussed

  1. Begin previewing the material before the semester starts.
  2. Read the introductory material and explore the book’s reference sections.
  3. Organize vocabulary, definitions, formulas, and theorems in a document.
  4. Read carefully, working through the meaning of each paragraph.
  5. Attempt worked examples with their solutions covered, revealing help only as needed.
  6. Return after a break and test what you can do independently.
Original Transcript (punctuated)

Based on the supplied transcript. Punctuation and paragraph breaks have been added, with repeated fillers and false starts reduced for readability. Unclear names or phrases are marked where necessary. The speaker’s opinions, personal explanations, and recollections are retained.

All right, kids. This is the podcast version of how to use a textbook. I’ll do a screen-recording version showing different textbooks. There’s a methodology and strategy to this.

Your college may not tell you which book you’ll use until the course starts. I say that if you aren’t two weeks ahead, you’re two weeks behind. That means starting to read two weeks before the semester.

A scientist is a professional problem solver. Some students say, “Nobody told me. How was I supposed to know? Can you answer my questions?”

Go back to the beginning: scientists solve problems. That’s why I object to private tutors, AI, Khan Academy, and solution manuals doing the problem solving for you.

A campus tutor or professor guides you back in the right direction. Like a train off its track, they put you back on the track rather than carry you to the destination.

If you constantly delegate questions, you’re acting as a manager rather than a scientist. There’s nothing wrong with management. I’m trying to help people find the right place.

Don’t push children into science because of Marvel movies or Iron Man. They may not understand the work involved.

For fun, I find an advanced mathematics or physics textbook, choose an unfamiliar question, and solve it. It can take days, weeks, or months.

The searching and connecting are valuable practice. Someone has connected these dots before, but I’m exercising the ability to find those connections.

That’s why the questions are called exercises. Like lifting weights, they build strength.

When someone else makes those connections for you, you aren’t doing that exercise.

The questions in the book have already been solved. They’re constructed exercises, and the book gives instructions for approaching them. Why use AI to solve them for you?

Let me explain using the textbook. First, your GPA shouldn’t be the focus for mathematics, physics, and engineering.

A medical or chemistry student needs something like a 3.8 because those are memory-based degrees. A mathematics, physics, or engineering student needs about a 2.5 on average, usually based on later courses.

If you obsess over GPA, you disrupt learning. You’re focused on a number that embellishes your ego.

The IQ test was invented in France in the early 1900s by—[unclear name]. I believe it was intended to identify people with intellectual difficulties.

I think the test is whether you fall into believing the number defines your intellect. If you think it does, you’ve failed that test.

There isn’t a test that can define your entire intellect. Who gives one person authority to decide another’s intelligence based on a set of questions?

Young people ask my IQ. I say, “You failed the test.” Then the argument starts: “You just don’t want to take it.”

All joking aside, GPA shouldn’t be about ego. A scientist should study with integrity, accept the grade, and focus on understanding.

I believe you can get a job or enter graduate school with an average around 2.5, possibly lower. There isn’t a line around the block for mathematics, physics, and engineering graduate programs.

If you want graduate school, stop cheating and stop obsessing over IQ and GPA.

I’ll demonstrate the textbook method with a screen recording. I may not do it today because I’m having two dental implants placed. Thank goodness for anesthetic.

They tell me to get Advil. I’m thinking, “Give me something real.” Anyway.

You need to be two weeks ahead. Mathematics-based courses can take 30 to 50 hours of study weekly. If you fall behind, that time is difficult to recover.

If a tutor carries you through, you may have to repeat the next course because you aren’t prepared. I’ve watched that happen.

Missing a week means trying to fit the missed work alongside the next week’s work. It’s like missing strength training and trying to double the load immediately.

Your brain is organic. You can’t plug in a cable the night before and download everything. Growth and recovery take time.

Be systematic, patient, and organized. During the semester, separate study time from family and social time. You can still have a life, but you need boundaries. I’ll discuss scheduling separately.

Being two weeks ahead doesn’t mean completing all homework and exams in advance.

Suppose you’re taking university physics and expect to use a book such as Hugh Young’s University Physics. You may not yet have the syllabus or know the assigned edition.

I’ve asked professors which book we’d use and been told they didn’t know yet. I eventually realized I could research the course or use an appropriate alternative temporarily.

I see that as part of becoming independent. The professor guides you toward self-sufficiency rather than being your self-sufficiency.

Physics books often progress by chapters, while mathematics courses may progress by sections. If you expect one or two chapters weekly, read ahead and work the examples in the reading.

I’m not saying to complete the entire exercise bank. You don’t know which questions the professor will assign, and the book may serve different disciplines and difficulty levels.

Solving many questions mechanically can make you good at arithmetic without developing the broader understanding.

Think of Sudoku: rather than solving one puzzle, I want you to think about creating a method that can solve the class of puzzles.

I show how to read the book, derive a method that produces an answer, and use another method to verify it.

Look at whether exercises appear at the end of each chapter or section. That helps you understand how the book is organized.

If you don’t yet know the assigned physics book, choose a calculus-based text for a calculus-based course or an algebra-based text for an algebra-based course.

Find a legitimately available copy. Don’t pirate. There are open resources, or you can buy a used physical book.

I prefer digital books. You need to learn to type and work with documents. I don’t think handwritten work prepares students for the technical document skills they’ll need.

I criticize the colored handwriting in online lessons because students need to move toward professional mathematical documents.

Suppose the course covers two chapters weekly. By week two, that would be Chapter Four. If the semester starts August 20, begin reading in early August.

Don’t study ten hours daily during the summer. Enjoy the break. Read a few paragraphs in the morning, afternoon, or evening, and try a worked example with its explanation.

If you expect to reach Chapter Four in week two, aim to have previewed that material by day one.

That creates a buffer if you get sick. Otherwise, falling behind can compound like debt.

If you miss the earlier material, it becomes difficult to do the next material. You have to return to it while the course keeps moving.

Successful students often figure this out. It’s okay if you haven’t yet.

Social media has shaped many students’ habits. I think parents should replace excessive phone use with preparation for independence: textbooks, cooking, laundry, and responsibility.

I believe giving children unrestricted social media is harmful. Give them a simpler phone.

I spent four hours on TikTok once, and afterward I felt like I did coming down from illicit drugs as a teenager. That’s my experience.

I call it digital crack. Parents should take it away and teach practical skills instead.

If they complain, I say, “Slap them in the face. Teach them how to cook.” Get a pot and pan and learn together. Turn off the television, walk, and talk.

Or you can spend your time swiping, judging, and arguing about what other people did. It’s profitable, but I find it disgusting.

Back to reading ahead: begin leisurely, then organize the textbook seriously before the semester starts.

I use text-to-speech because I can listen while cooking, doing yoga, or other activities. I’ll demonstrate how.

Before Chapter One, start at the title and read everything: the foreword, preface, and other introductory pages.

Then inspect the material after the final chapter, including appendices and the index.

I highlight the text and have it read aloud, even index entries. I don’t expect to understand every term immediately.

My explanation is that learning happens in layers: encounter a word, learn its definition, and later understand how to apply it.

I like hearing the vocabulary first so it feels familiar when I meet it again. Then I connect definitions and applications to it.

I may listen while cooking, doing yoga, or walking the dog, depending on whether the document will play on my phone.

I’m not trying to understand everything at that stage. I want the words to be less unfamiliar.

You can skip an answer bank consisting only of numbers, but look through the appendices, index, preface, and the rest. They’re included to be used.

After that, open Chapter One and a Microsoft Word document.

Collect the bold vocabulary terms and their definitions. I use a bulleted list. You can copy the definition into your study notes or rewrite it in your own words.

Then go through again and collect formulas, theorems, and equations.

Take a break. Later that day or the next, listen to the chapter through text-to-speech.

Again, my goal at that stage is familiarity. I think of letting the mind process the material over time.

Now I have vocabulary, definitions, formulas, and theorems collected. I’ve previewed the chapter and the book’s surrounding material.

Then I begin the careful reading. Start with paragraph one. Don’t move to paragraph two until you understand paragraph one.

The opening chapters can take the longest even though the material seems easiest. They establish the foundation.

If you don’t build that foundation, later work can sink into the mud. That’s why I recommend beginning before the semester.

Don’t turn this into a stressful ordeal. Think of it as stretching before lifting weights. You’re organizing the material.

I’ll demonstrate my files, organization, notes, and preparation step by step.

Read paragraph by paragraph. In my experience, investing time in the early chapters makes the semester easier later.

People have told me they followed this approach, studied less, understood more, and had an easier semester than expected.

I tell them, “Send me some money.” Having integrity isn’t good business in this world.

Next, when you reach a worked example, type the question. Cover its solution and try to solve it.

If you can’t, uncover a small piece of the solution. Continue until you can reproduce the reasoning without looking.

Take a break and return. Give yourself a short quiz.

If the exam will be handwritten, practice with pencil and paper. I’ll discuss practice exams in another video.

I think instructors should move toward typed examinations. Students need to prepare professional documents, and I believe computer-based exams can be proctored without internet access.

I consider continuing to require extensive handwriting harmful and outdated. I want to explain alternatives to instructors.

Students need to become proficient at typing mathematics. I think copying, pasting, and mathematical input in Word can make it much faster than handwriting.

I’ll show the actual notes and demonstrate the process in a screen recording.

High-school teachers have had access to this technology for decades. Students need document skills by the time they enter the workforce, and I think instruction should reflect that.

That’s how I approach learning from a textbook in college.

Subscribe, become a member if you can, leave a Super Thanks, or buy a book. I appreciate it. That’s how I pay my bills. Without your assistance, I can’t do this. Have a nice day.

AI Summarization

Author Jonathan David presents a structured textbook-study routine built around early preparation, organized notes, careful reading, and independent practice. His phrase “two weeks ahead” refers primarily to previewing and studying material, not completing future graded assignments.

Begin Before the Semester

Jonathan recommends starting with light reading before classes begin. His aim is to establish familiarity and a buffer so that new material does not arrive entirely unprepared for.

Explore the Book’s Structure

The proposed preparation includes introductory pages, the preface, appendices, and index. Jonathan treats these as a way to see the book’s vocabulary, organization, and supporting resources before reading the chapters closely.

Build Organized Notes

He recommends using a document to collect bold vocabulary terms and definitions, followed by formulas, equations, and theorems. He plans to demonstrate his file organization and note-taking process in a separate screen recording.

Use Text-to-Speech for Previewing

Jonathan describes listening to textbook material while doing other activities to become familiar with terminology. This is presented as his personal previewing method; the later steps still require attentive reading, explanation, and practice.

Read Carefully & Work Through Examples

The close-reading stage proceeds paragraph by paragraph. For worked examples, Jonathan recommends covering the solution, attempting the problem, revealing a small amount of help if necessary, and repeating until the reasoning can be reproduced independently.

Return After a Break

A later attempt or short self-quiz checks whether the method can still be used without looking. Jonathan also recommends practicing in the format required by the actual examination.

Develop Technical Document Skills

Jonathan strongly favors typed mathematics and professional document preparation. He discusses Microsoft Word, mathematical input, and his preference for computer-based examinations.

The study schedule and time estimates reflect the speaker’s recommendations. His broad claims about GPA thresholds, graduate admission, IQ history, and learning mechanisms are not established by this discussion. Actual course rules, admission requirements, and individual learning needs vary.

Explore Mathematics with Math Monthly

Explore mathematics, physics, and their connections to engineering with Author Jonathan David. Discover the available memberships and follow the development of new lessons and journal material.

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