How to Get Better at Reading Math Books

[@louisedarby2761]

Thank you for your advice, I also struggle with reading maths textbooks and I am 52. My main issue is how to take effective notes from a textbook. It is a skill I don’t think I was ever taught or if I was I have forgotten. I have seen loads of videos on taking lecture notes but no textbook notes. I am sure everyone will think I’m daft but I am struggling with a maths degree because I get lost almost copying the entire textbook into my notebook. If you have any advice I would be very grateful. Many thanks Louise Darby

[@TheMathSorcerer]

I will make a video on how to take notes from a textbook:) Thank you!

[@helms6561]

28 here and I am THE EXACT SAME WAY! -- Lucky for me I am post my degree so I can learn at my own pace. For people like me who only learn things by doing it the hard way; I recommend this method. --Doing all the example problems and Practice problems, doing all the "This is left as an exercise to the reader" or "The reader is encouraged to work through the derivation themselves". I understand the struggle; getting through most of any textbook in a condensed semester while still passing the course is damn near impossible (For that I recommend watching videos and learning the Feynman method/technique). To put it into perspective I spend 4-5 hours a day on the weekends and some weekdays, and I'll be happy if I get through three - four pages in a text book. I remember spending 8 hours on Cauchy's Equations for Stress Tensors, and I have spent countless hours on Navier-Stokes (my greatest weakness/downfall will be physics based vector field equations and actually mapping them out).

[@Domi59]

I can tell you what I do: I try to filter out ideas and connections. What is the idea behind the definition/proof/example? Are there connections to stuff you learned before? Write those things down. Example: In linear algebra you define "vector spaces" and you have a big lot of axioms. A little bit later you define "sub vector spaces" by like 3 axioms. After I understood the concept, I would maybe write notes like this: "Subset of a vector space which is itself a vector space with the same operations." "Cool thing: If I want to check that a subset of a vector space is itself a vector space, I only need to check these 3 axioms instead of the million axioms of a vector space". I have to add: you will likely not always be able to find an idea or a connection lol And most of the time you will find those things when you revisite the page when you have more knowledge

[@michaelb4727]

I've definitely had the same problem. For what it's worth, what works for me is to read the entire chapter or section without making any notes. Then, sometime within the next few days (maybe even later that day), I'll go back through the chapter and make notes. This generally gives me enough perspective to know what the key ideas are. Because I'm studying for personal learning on my own time, I only make notes of things I _want_ to be able to recall-usually the important or interesting things. I've also made a deal with myself that I'm not responsible for remembering anything that I don't have written down in my notes, and this has freed me from a lot of anxiety. To summarize, if you find yourself writing down everything, the material is probably too fresh in your mind to where everything seems important, and the key ideas haven't had time to bubble to the surface. I just finished reading the first half of Tom Apostol's Calc 1 book, and I decided to read straight through over the course of several weeks without taking notes or working exercises, and am only now going back for a second pass to make notes and do exercises. Naturally I don't recall the material completely or know how to work the thornier problems, but I have a really good idea of what the key ideas are, and the typical pattern of the proofs. This is kind of an extreme example, but the subject matter I've covered (integrals, derivatives, and continuity) is all related, so I wanted to see how it all fits together. Also, even though I completed a math minor at university, I never learned how to write proofs (and only vaguely followed along with proofs in class), but I'm quite interested in seeing _why_ calculus works, so I'm working through them all. This has proven challenging, which is part of why I'm not making too strict a requirement on myself the first time through the book. But I'm really enjoying it and learning a lot, and to me that's what matters :)

[@ItamarOliveira]

I'm 51 and also struggling here!

[@steveschmidt5156]

When I read a math book, I visualize myself explaining it to someone else. This helps me to remember material at a semantic level.

[@WitchidWitchid]

YES!! That has worked for me for what seems like ages.

[@nickolaussoerjono2734]

Interesting - I notice myself unconsciously doing that when trying to understand something. It does work really well!

[@kaganozdemir4332]

you cannot understand something you can't recreate. either you should recreate what you're studying by performing a task or re-create the material as an explanation for another person.

[@danielpalmer643]

I had one professor who always emphasized that "notation is trivial". I think it was really good advice for reading math. Different people prefer different conventions. It's more important to read the math than the text usually, so figuring out what the notation means is important, but that part isn't usually complex. The goal of notation is to make complex things easy to read.

[@stephenoconnor6180]

On the note of focus. If you are anything like me and struggle with getting started in complete silence: put on some music (ideally instrumental, but not strictly necessary), find the sleep timer function, and set it for about 5-10 minutes (depending on how long you’re studying). I find this helpful in slowly transitioning into that more focused state that is really good for mathematics, rather than just jumping straight into silence that you have to endure for 30 MINUTES. It is also a good metric for how engaging the material is. If you never notice the music turning off, or you do but you don’t stop studying to restart it, that’s probably a good indication that something is clicking. Whereas if you spend 5 minutes staring at the page, restart the music, 5 more minutes staring, restart the music, 5 more minutes, etc., then that probably means you need to take a step back and reevaluate what isn’t clicking.

[@PeacenLuv777]

I think a video on notes would be a perfect video in your normal style, but I would love to learn more math in long form style through your videos, especially going through a chapter and maybe having some be guided by you and other parts are self guided. Maybe getting us up on our feet and letting us go from there.

[@TheSoundofSilence343]

I can’t speak to tertiary maths but this is what helps me for more basic maths that I am struggling with. Watch KZbin videos on the topic. Watch all of them because each presenter has a different technique and some even drop little shortcuts or even just particular phrasing that will suddenly just click with you. You can take notes from the videos just like lecture notes. Then do lots of worked examples. Have a sound understanding of the basic concept and then go back to your textbook and read and take notes in your own words and do all the questions, examples provided. If you are still struggling after all this, wait a few days for your brain to relax and consolidate the inputs and then start all over again but this time it will be faster and easier.

[@shoaibislam7056]

I would actually LOVE to watch you go through a book chapter by chapter!

[@ahmadibrahim7932]

Man I can hear you for hours taking about maths it's too soothing.. 🥰

[@martinhawrylkiewicz2025]

Great vid! This is how I "read" a math book like Velleman's (my current"read")...I have my marble notebook dedicated to every book I am studying...and I underline important definitions, concepts theorems, write the definitions down in my notebook, and try my best to understand the concepts, do the exercises! Like Prof. Halmos said....don't just read it...fight it!

[@crown_420]

Comprehension is an overlooked technique. It is important in learning, as having a higher level of comprehending ability enables to grasp complex ideas and information. I think knowing the underlying meaning of each word, with other techniques, is helpful for easy comprehension.

[@edwardsmith-rowland2852]

Get a few sheets of blank paper and a pen. Write the equations as you read them - even if it's just copying. Sometimes seeing the symbols in your own hand helps take ownership and start the flow.

[@StaticBlaster]

Thanks for responding to the email and making a video on this topic because I have a difficult time reading math books as well. I never really understood the Velleman book in its entirety. Discrete math and proof writing is a complex subject to master. And I would consider myself a noob, still.

[@douglasstrother6584]

Draw diagrams or geometric interpretation of the topic. Visualization is powerful.

[@daniellindner826]

I was waiting for a vid like that. Thank you for this. This will improve my reading of math books further.

[@timthompson468]

What I do is take notes by rewriting whatever text is written in my own words. It is time consuming, but, by rewriting the text in my own words, I can’t move forward until I understand the topic at hand. Of course, I also write the equations and formulas and include any extra notes to remind myself of what the notation means. I used to do this with pencil an paper, but now that math software is available I use that so I have an electronic record of my notes. I’ve mainly used MathCAD and Mathematica. The beauty of that is it is then possible to explore the concepts further than the book goes. Sometimes I like plotting expressions to see what they look like even if the book doesn’t discuss that. Another advantage of using computer algebra systems to take notes is you quickly become proficient in using the software.

[@erickroeger1161]

I prefer books that have immediate exercise(s) per subject/concept compared to textbooks that (notoriously) pile subjects and leave the exercises at the end of the chapter. For me its better if things are presented and worked in small doses; especially if I'm just studying in 30 mins.

[@dimitrioskalfakis]

i am a visual person. whenever i study math related material i need to be able to draw and write stuff on a piece of paper that will help me visualize and understand concepts. if you need to utter aloud the content read do it. each person is different. find the proper way of dispensing the material to you brain.

[@martinhawrylkiewicz2025]

Great vid! Another awesome book is Book of Proof by Richard Hammack...I think it has more examples than the Velleman's book and more diagrams, visual aids. I am very visual person so I am always looking for that in math books...otherwise I am always supplementing textbooks with my own sketches of diagrams, functions, venn diagrams, etc.

[@hipobert]

I would sit through a 45-minute video of guided reading with you!

[@selene3021]

You're my favourite wizard.

[@andisteiner3494]

Please do the video on working through a chapter! Even if nearly nobody watches, maybe a few people get an inspiration.

[@tgkmervin5998]

what I would recommend is to learn all of the fundamentals such as algebra and trig and make sure your totally comfortable with the two then calculus should be easy that's how it was for me after looking back at algebra 2 and trigonometry I realised I don't know as much as I thought I did so definitely look over that stuff and maybe do some research on pre-calculus then that way you'll be familiarised with the notation as well. This is what helped me get through calculus. (But the key things to keep in mind are; taking a moment to understand, fundamentals, practice.)

[@UshiromiyaSebastian]

Hi! i think that besides what you said, is important to step back a little bit sometimes and get used to read math symbols like "for all" "for every" etc and to understand what every operation means. It makes a HUGE difference when you start to understand what the formula is trying to say instead of memorizing it.

[@dr.michaellittle5611]

I’ve found that the best way to read a math book is to have a pen and paper when you do and write down what’s being taught in the book, and work the problems. It helps build muscle memory so to speak.

[@shreyasood2457]

While studying maths I handle this by diagramstizing and labelling the proofs and derivations, for symbols and substitution of value or formula made. It helps create sketch notes and flowcharts for studying maths concepts.

[@AceOfHearts001]

As the writer of the email is doing the UK qualifications, it gives me the chance to say the following. I would like to kindly request the Math Sorcerer to review the set text books for A Level Maths and A-Level Further Maths! They are called Pearson Year 1 and Year 2 A Level Maths. A search should reveal them. Further Maths A Level books are called Core Pure Year 1 and Year 2. There are also the applied modules books (Statistics and Mechanics) for the courses. I personally think those are some of the best, most readable textbook I have seen so far on Mathematics and I have often thought about what your review might be on them if you saw them. This was my chance to put in the recommendation!

[@crazyfly5505]

Would you please do a video on all the math, in a recommended order of study, with a brief totally ignorant person's explanation of each area and how that portion of math may relate to the sections before and after it? For example "combinatorics" means absolutely zero with no frame of reference. A brief search returns "Combinatorics is the branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their properties." This is probably a brilliant explanation if you already know what combinatorics is. I know I'm probably asking a lot but it would be so helpful for me, as someone with an interest in number theory, if I knew what I don't know so I know what to study. You know? Thanks MS! Sincerely, an old guy who spent too much time smoking in the boys room.

[@Mosaic_Official.x]

Please do on how to take notes from a book.

[@StaticBlaster]

computational math is really just memorizing axioms and theorems and applying them to word problems and what not. Abstract math is about understanding why the theorem and axioms are true.

[@parrotraiser6541]

One omission from almost every math book is an explanation of how to ponounce symbols and voice expressions. (Especially when the author has invented them or used in an unorthodox way.) If you can't read the text out loud to yourself, how can you study or remember it?

[@StaticBlaster]

I think Brian Cox uses "maths." I'm pretty sure it's common in the UK.

[@danielmrosser]

Erdos 6:01 is pronounced “air-dish” I recommend the wonderful biography of Erdos by Paul Hoffman called The Man Who Loved Only Numbers

[@sicko_the_ew]

If there's an "o" with an Umlaut on it in his name, and it's used in the German manner, "dish" is also not right. The "i" would sound something like "er" in this case. (I suppose the easiest is to go to KZbin and find a nice, misleading yet confident video to hear it, there. :-) )

[@danielmrosser]

Indeed thank you. Yes it’s a bit tricky. Air-dish is closer to the mark and seems like the closest phonetic representation of the correct pronunciation but I’m open to seeing a better one

[@timbuktu8069]

I have a similar problem with government/military acronyms. A pamphlet might refer to the Department of Redundancy Department ONCE and from then on just call it DRD For math, I would say reduce what you're learning to the most basic that you can handle (+ - =) until you feel comfortable then add on. There is no shame in not knowing something.

[@rubencollazo8857]

I would watch a 45 minute video of you reading a chapter out of math book!!

[@Jabbaerwocky]

Good stuff! Keep it going!

[@Adityasingh-mw5zp]

Sir, I'm from India and I found your channel recently I watch your videos everyday and I really attached with you in the journey of maths through this channel. I will complete my class 10 within a and will be prompted in class 11 and I want to go with maths. Sir I really want some suggestions from you,I want to strong my basics and wanted to learn all the branches or topics of maths and I really need your guidance.It's my request that you give me some advice..

[@aryansrivastava727]

Do not do not do not go for books like cengage or arihant series for maths rather more books you read, the more ideas repeat the more you will remember always choose multiple books for algebra, calculus ,trigno etc and do not stop...even if you cannot understand something its ok move on to other topics without thinking or read it from other books , do not think that doing jee books will help or do not think of time constraints just go for it

[@officialgmanlynx]

I'd sit through an entire series on a single book if you do the apostal Calc vol 1 + 2

[@noam65]

Being dyslexic, I've often struggled with focus issues in many different types of reading, maths probably most of all. I'm an American, who grew up saying math, however, the correct word would be maths, as the correct word for little metallic disks of monetary value is the word COINS, rather than coin, for multiple value types. In this same way, MATHS is correct. Mathematicians apparently aren't generally linguists.

[@tobyearth]

I would love to listen to you read from a math book. Did you ever end up recording videos of this nature?

[@nikp941]

I find calculus books difficult to read because when author provides example based on the topic he skips steps and I find myself trying mentally fill this gap ,by solving example ,to comprehend how he got to the solution. So I just skimm chapter and focus more on practicing.

[@sutriadikurniawan4097]

thank youu,

[@eusouogreg.4516]

Hi, great video, can you make one video about your worst math books colection?

[@TheMathSorcerer]

Great idea!

[@Jackrobert28]

@@TheMathSorcerer Hope you start saying Maths - love your channel from the UK.

[@hhandle]

i will read as if there's only one page in the entire book so i dont get overwhelmed by the number of pages so ill take it one page at a time and i also imagine that words start to appear magically as if the page was blank before i start reading or seeing it ps: i do all this to make reading good so i dont feel the boredom

[@lisareed5669]

I was thinking about "maths" the other day. Think about: we say "mathematics." So, not outrageous. It's a British usage.

[@Meghana_Nallamilli]

I feel like I get lost just watching videos on book recommendations and some topics/hard questions but I miss covering the breadth of the subject- either that or I just get a high level overview of everything but can't get myself to do what is assigned and required for completing a standardized course. I end up with a very staggered understanding of topics- either one idea that I happened to spend a lot of time on that seemed very interesting or just information on what all topics are (just learning vocabulary but not exactly understanding what it entails, I've also started treating some topics like history and just download books but never happen to read them fully). How should I go about approaching a subject from an academic standpoint and building the required mindset?

[@captainom5065]

do it i love to see read a book

[@brianmccormick8328]

I have that book too. Excellent for a self learning person like me.

[@petrih8332]

Where did you get that Sorcecer figure on your desk? I think I need one on my study desk to remind me of your principles:).

[@aaronwong7340]

In Australia we say Maths

[@bluedragontoybash2463]

Any tips on how to read Math olympic prep books?

[@NoobleeGt]

Hello, I got two questions : Is there a reason why "How to prove it" would be recommended more than "book of proofs" or "proofs" by Jay Cummings? Second, would you recommend "all the math you missed" for a non mathematician? I mean, in Control system engineering, there are a bunch of mathematics, but you don't need to know all the details like a math major would do. The ideal scenario is of course to know math at a graduate level, but time is a limiting factor. So, is this book a good way to go to be able to study more advanced topics in engineering without having to be concerned too much by mathematical knowledge? Maybe you could answer this in a video for physicists and engineers ;) Thank you for your videos!

[@TheMathSorcerer]

I like that the Velleman book is smaller(in physical size). Yes it's a great for anyone:)

[@ronaldjorgensen6839]

NICE ABOUT MATH YOU CAN FOLLOW TEXT AS WELL AS GRAPH THE MATHS TO ME IT HELPS UNDERSTANDING AND MEMORY BOTH story lines same topic

[@gvi341984]

We need books on FE/PE exams and calculator advice. Math is not so bad once you have to remember all the formulas and conversions are a problem

[@thomasblackwell9507]

For the FE get a Technical Physics book and work all the problems in it. The problems in the morning portion are generally not that complicated. This is what I did back in 1991. As far as the PE exam; what specialty are you taking the test for?

[@gvi341984]

@@thomasblackwell9507 Not taking it but these types of books are important and so are the calculators

[@tiago.alegria.315]

How to think like a mathematican ( seems a good book)

[@kx4532]

Don't use Erdos'es method of focus

[@vipham2158]

I just fail my math test 😅😅 and lost the change to get in university😢😢 . The pressure make me fell depress

[@vincentzevecke4578]

This is normal

[@mujeebrehman0178]

Can I read this book I am in 10th standard

[@rationalsceptic7634]

Maths is short for Mathematics

[@rito_ghosh]

I strongly advice this person Pomodoro technique. And not to try to read Math for more than an hour a day.

[@aligatoryisus9865]

let's goooo

[@UBE481]

Sir can you suggest chemistry books please.🙋‍♂🙋‍♂🙋‍♂🙋‍♂🙋‍♂🙋‍♂🙋‍♂🙋‍♂🙋‍♂🙋‍♂🙋‍♂🙋‍♂🙋‍♂🙋‍♂

[@joshux3210]

I wouldn't mine watching someone studying math for 45 mins

[@SeemaYadav-io4qt]

Good morning sir ji

[@NathainArdoin]

may the Force of Maths be with you All going Forward.. May the symbols make sense and the integration into the parts of maths be full of fun and not just vocabulary, the problems are there for your mind to work towards an answer whether it be for your breakfast mix of pancakes or your taxes need are now 8% and not 9.5%, therefore, the language you are learning is in every part of your life and will always be there, up to you to unlock the definitions through careful practice following the Limits as they come and taking notes of their derivatives, the matrix of life is exponentially better than a square or a cube....... the topology of breakfast assures us the coffee mug handle is just......... needless to say Lyn........... may God bless you and your efforts to become knowledgeable about Maths........and Math's fields.......

[@moncefnafti1877]

real

[@cherrycityhero]

I subscribed your channel it keeps unsubscribing again and again. What is happening

[@jimpim6454]

Its British English: maths.

[@NathainArdoin]

how about ALL OF THE FORMER BRITISH CROWN....................... and the five eye countries use Maths.........

[@TheSoundofSilence343]

Australia = Maths 😊

[@powermonger9090]

Yep, Math just sounds wrong.

[@keithdow8327]

How to prove it has a third edition. All the math ... has a second edition.

[@rusi6219]

The posterity of editions

[@Number6_]

Maths is shortend from mathematics. While math is just singlular.

[@richardcasey4439]

How to Prove It is an excellent book

[@ndotl]

"Maths" drives me crazy. Also, you are wrong. When I was in school (in the US), it was "math", even though "mathematic" is never used. What is used is "mathematics", and the "s" is not an indication of plurality. So adding the "s" to "math", which the US did at some point, was unnecessary. Having said that, it may have been done to be consistent in international studies. What else grinds my gears? "Gigs". In the US it used to be "gig", "meg". If you do not abbreviate, you would obviously use gigabytes or gigabyte. Correct Examples: What is the size of your drive in gigabytes? I have a 30 gigabyte drive, or, I have a 30 gig drive. Incorrect Examples: I have a 30 gigabytes drive, or, I have a 30 gigs drive. Clearly this is an opinion, and one of many.

[@volcaphft]

play piano before learn math helps me focus