How To Learn Mysterious Math Symbols

Some people say math is another language because there are so many symbols and things that you have to learn. In this video I answer a question from a viewer. His name is Nathan and he is asking how to learn Math Symbology. I suggested a few wonderful books on proof writing which I've linked below. Do you have any advice or opinions? If so, please leave a commebt below.
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Thank you:)

[@aarondriscoll287]

Proving The Math Sorcerer plays Magic: the Gathering is an exercise left to the viewer.

[@santiagomedina8585]

I just wanted to take a moment to express my gratitude for all of the inspiration and motivation you have provided me. As a PhD student in computational biology, in Mexico, I have always been interested in math, but your videos have truly pushed me to dive deeper into the subject and learn more. Your enthusiasm and passion for math are contagious, and I have found myself staying up late just to watch one more of your videos. Your ability to make math fun and accessible has been a game-changer for me, and I am so grateful for all that you do. Thank you for being such a positive influence in my life and for helping me to become a more confident and capable math learner.

[@imanolfernandezdearroyabez2489]

What did you study previous to your PhD?

[@ahaszsaddssd9931]

Where do you pursue it? I thought computational biology in Mexico was not very common

[@ntvonline9480]

The context of the course can determine the meaning of symbols. There is a finite number of symbols in math so that they get used again. For example the absolute value notation is used to find that in an algebra class, but it is also used for distance in calculus or order in set theory. Make sure you read your textbook or lesson introduction because that is usually where the definition is explained.

[@TheMathSorcerer]

Excellent comment! Context is king!

[@eflat6522]

Timely video for me. My copy of How To Prove It should arrive at my door Monday. I can't wait.

[@christophermball]

While proof books are a great approach for demystifying symbols, a more direct approach (especially for engineers) is to pick up a copy of the small book "Mathematical Notation - A Guide for Engineers and Scientists" by Edward Scheinerman. I originally picked this up for the same reasons ;).

[@TheMathSorcerer]

Oh interesting, thank you for this comment!

[@danilo666]

Hey! in Computer engineering we do Math a lot of, Discrete Math overall but we discretize functions and do numerical methods. Also we have formal methods for software correctness and those are like a proof. We use induction and the well order principle as well

[@30803080308030803081]

I think your advice is good. If Nathan works through one of those books, then reading math will become easier for him. Moreover, this is the best preparation for going on to study any math book on a specific subject at the undergraduate level.

[@ItsKingMyles]

my favorite math excerpt was applying statistics to optimal magic deck building strategies.

[@jennifertate4397]

The Harper Collins Dictionary of Mathematics is a great thick and compact softcover book, approx. 8" H x 5" W, with extensive definitions and cross references. In the Appendix, there are 9 pages of math and logic symbols. I highly recommend it overall for mathematical studies!

[@yash1152]

> _"Harper Collins Maths dictionary"_ hmm, by name, that seems the correct thing. Thanks for recommendation.

[@jennifertate4397]

@@yash1152Your welcome. The title I gave is for the US and Canada. Enjoy.

[@coffeeconfessor4747]

Ooh thanks!

[@jennifertate4397]

@@coffeeconfessor4747

[@knowledgeispower.k.haripra3119]

Good morning sir and thank you very much from the India.

[@daniellindner826]

Great video, congrats on hitting 500k!!! I follow you since 100k. Thank you for making a short review on the chartrand proof book again.

[@AutomationDnD]

*_There is a Lack of Rigor_* .... I believe that THAT is the Old Phrase, used in describing an adherence to disciplined thinking/teaching/explanation (I just Like word-play & etymology, so when you were trying to describe what is LACKING in some videos.....) Lately I've been paying more attention to math based channels (& buying a few books to reLearn things)

[@ivanperica3731]

Your channel was weird for me at first. But after a couple of videos I enjoy it very much. Congrats on half a mil, very well deserved. Also, I was wondering, do you have any book recommendations on math or pshilosophy logic?

[@God-ld6ll]

I take the "Math is a language", rather a loose saying. Fp or "First principles of first principles." as a guess of mine.

[@yuvrajsingh099]

Great Video. Can you please make a video about computer science (introduction/ begineer type books like algorithm, flowchart, common terminology etc).

[@ndotl]

At 1:50, I am thinking 1: Greek alphabet, and 2: logical operators. For 1, you can find that on the Internet. For 2, in the Chartrand book chapter 0 section 4 is titled "Using Symbols". Here, (for example) the quantifiers are introduced. Also, for (2), I would think most introductory logic texts (e.g., the Chartrand book) introduce the symbols before they are used. With some digging you are likely to find one that also lists the symbols at the beginning of the book (I know I have seen this. Could have been a discreet math book.).

[@yash1152]

umh, greek symbols are okay to know, but often they have specific meanings, like π (circle constt), Σ (summation), Π (product), Δ (difference) and so on... i have seen books with list of symbols too... but that is as brief as it can get. Lacking any detail.

[@janplonka7143]

Math and mtg, my two favorite pass times

[@minimalrho]

I've been trying to read some calculus books to make recommendations for students, but I have some difficulty reading material that I pretty much know already. I was wondering if you had any advice for reading through material you already know and assessing if it's good for students.

[@metildajoseph5265]

Greetings Mr.Professor, Thoughts : - Good, Simple Textbooks invoking knowledge of Mathematical Science. Response : 'Mathematical Symbology is the Key Note of Maps in the Field of Science in every aspects'. Thanks.. Take Care,Professor.. With regards, RanjithJoseph (R.J)

[@rich_in_paradise]

A lot of math texts for applied subjects have a summary page of symbols in the front or back. You can also hit up wikipedia - they have a master page titled "List of mathematical symbols by subject". Personally the thing I struggle with is verbalising (I always like to think out loud) equations that use greek letters. That really slows me down when reading papers. There's no solution to that than just getting a chart and memorising them.

[@azimuth4850]

I really need to start a Proof book. I might go with the Velleman one.

[@danielpalmer643]

One professor always told us, "Notation is trivial". I think that idea helped me a lot. I think one thing that can also help is looking at math historically. Notation style comes from the ways earlier mathematicians chose to write. Notation is kind of like fonts in a word processor. There are many ways of writing a derivative, for example. Perhaps most symbols in math can be varied. However, I agree that a lot of this stuff comes from formal logic notation. All of those upside-down A's and backwards E's will help you with both Aristotle and Calculus.

[@jamieg2427]

see the famous essay "Notation as a Tool for Thought" by Iverson. the first few paragraphs contain a summary of thoughts of famous thinkers about notation. notation is trivial because we have decent notation that we're used to, but that notation exists probably because without it, expressing certain ideas was nontrivial. feynman diagrams, vectors, tensors help us package ideas to be more digestible, removing noise. even basic things like the order of operations didn't always exist, isn't strictly necessary, and has a surprisingly powerful simplifying effect on how math is written, allowing us to implicitly chunk parts of equations together. good notation can better highlight patterns and relationships. powerful notation can alter how we consider ideas and problems and even suggest new understandings. derivatives are sometimes written as an apostrophe, like f'. roman numerals are sometimes used at higher derivatives, which is a change in notation. that notation then might make you wonder, if integers can be used go indicate derivatives, what about rational numbers? what would fractional derivatives mean? what about derivatives with a complex degree? note that there's a parallel to exponents, and that we indeed found a use for exponents, even imaginary exponents. en.m.wikipedia.org/wiki/Fractional_calculus

[@coffeeconfessor4747]

When I take notes, sometimes I use symbols that make sense to me and then translate when I rewrite my notes, I use proper symbology

[@juaneliasmillasvera]

My advice to the person who made the question is that he should get also a dictionary of mathematics (for example the Oxford basic one is very cheap), in that dictionaries at the end it usually has an index of symbology, like 8 pages long classificated in topics. I have been always interested in mathematics notation and where the symbology comes from, that is why I have read a lot of profesional made tables of symbology and have read about history of mathematics. By the way, congratulations for the half million subscribers Sorcerer.

[@devon9374]

I’m an engineer and I agree with your point about it being harder. We have to deal with the real world and have to use math, physics, programming as tools (sometimes when we are taught math, the beauty is glossed over). I think the teachers are harder because if you fail in engineering it can often mean death.

[@jamieg2427]

while exploring proofs is worthwhile, a faster solution is reading through this wikipedia entry: en.m.wikipedia.org/wiki/Glossary_of_mathematical_symbols there's not as much as one might think, and it can be read in a single sitting, then reviewed a few times in the following days. once done, you may find that the difficulty was deeper than the math symbols. at that point, leaning into proofs will probably be the next step.

[@dimitrioskalfakis]

it's not hard tackling a subject at a time but attempting to do it across a large variety simultaneously is challenging to say the least, unless you are a seasoned math major. so, my advice is to concentrate on either calculus or numbers or sets etc. but one at a time.

[@Anonymous-qw]

I did a Bsc(Hons) in Mathematics in the UK in the 1980s. I had friends that were doing engineering and some the calculations I saw they had to do I thought were really difficult.

[@StaticBlaster]

I used the Daniel Velleman book in my discrete math class in my fifth semester.

[@manishrai9170]

Sir I am from India. I heartily want to be a mathematician and currently I am studying in class 11th so would like tell me how can I be awesome in maths and to take at it to advance level where no one reach specially those who are currently studying with me❤️❤️🙏🙏🙏

[@georgephillips2600]

I always underestimate my mathematical abilities, and in reality struggling in math at times can make me sad depressed and even suicidal. The main reason why I doubt my math abilities is because I have a mental disability otherwise known as (autism) spectrum disorder I don’t think that god will never open the doors for me

[@TheGuruNetOn]

Reminds me of the term "Idiomatic code", "interface layer" and "design pattens" used in Software. Low Level Blocks (Cryptic, Implementation level) Middle Level Blocks (API, Abstract interface giving a Semi-Logical View of a set of operations) Higher Level Blocks (Logical Level, Uses Middle level blocks to carry out high level solutions) Some of the notation comes from bottom-up constraints of a particular language. So lower level blocks of code are more cryptic and implementation dependent. But as you go higher and write more logical blocks of code it's more of a top-down approach where you breakdown higher level concepts into smaller mid-level blocks. The mid-level blocks abstract out the implementation details and offer push button interface to the highest level blocks. In Math it's quite difficult to distinguish which layer you're dealing with LowLevel, MiddleLevel or HighLevel. Unless you're good at it already, of course.

[@ronaldjorgensen6839]

THANK GREAT VIDEO AND RECOMENDATIONS

[@LorenzoWTartari]

A "shortcut" could be the dictionary of mathematics (don't remember if it's published by Collins, Oxford or Cambridge)

[@kevinreese5656]

I'm assuming based on your coasters that you play Magic. Any chance of a video on how you experience the greatest game ever invented as a mathematician?

[@paulheinrichdietrich9518]

Well I suppose they are related to some degree, after all wasn't Richard Garfield a mathematician?

[@heferh4320]

I'm reading a book about logic and how to write proofs, the book that I have Is very rigorous but i like it more than others beginner friendly books because the only thing that you have to do is re-read definitions and think. The other books sometimes lie a bit at the start or dont tell "the whole story", and that is (sometimes) more confusing haha

[@edilebert]

What book is it?

[@heferh4320]

@@edilebert "Basic mathematics" by M. Lázaro C. unfortanely, I think it's only in spanish but you can try using an online translator (for reading some concepts) there is a PDF version

[@Mathematica702]

Princeton Companion to Mathematics. Is that not an epic codex if there ever was one? Have you seen this huge compendium of pure math? I wager you will not find a book with more math on this planet. It includes small biographies of all famous mathematicians & their work.. an index of historical & open problems, articles on what seems every conceivable subject & it’s origins.. branches upon branches of elucidations.

[@martinhawrylkiewicz2025]

Great advice! I took your advice and am currently focusing my energy on learning the foundations (set theory and logic) using Transition to Higher Mathematics book by Smith, Eggen, and Andre. I got it really cheap used from ebay for less than $10. Great for self study.

[@TheMathSorcerer]

Oh that’s such a good deal!!!

[@TheMathSorcerer]

Awesome!!!

[@martinhawrylkiewicz2025]

@@TheMathSorcerer I got the 3rd edition with some pencil markings inside but still almost like new condition. Love it.

[@argonwheatbelly637]

Math is a language; hence, it's an art. But that's me. Also, love the MTG coasters. "Untap, upkeep, draw."

[@Hofer2304]

How would you say a * b + c and a * (b + c) It is very likely that you say both expressions in exact the same way. Or consider a function f(a, b+c, d & e) You can say and for both the + and the & . Or you say for the + plus and for & and. Certain ways to say an expression can it make easier or harder to understand the expression.

[@fahimmahmud4659]

Congratulations for 500k subscribers 😊😊.

[@TheMathSorcerer]

Thank you!!

[@hatoline4731]

Whoever wrote you that letter I am in the same boat and grateful.

[@danilo666]

In the other hand I had a difficult time reading Foundations of Geometry by Hilbert even I was not able to finish that one :(

[@sicko_the_ew]

Long before I ever attempted calculus (which has a scary name to a phobe) I picked up a secondhand book on algebra (which has a less intimidating name to a phobe). Turns out it was "abstract" algebra, whatever that is. They accepted nothing as obvious. They proved all the obvious things (which was quite interesting). As you might imagine, I made extremely slow progress through the book, and not much has stuck. (Nothing of substance has stuck - unless it got incorporated into what I learned of other things, later, in the correct order for learning these. I remember there was much made of sums of products, and products of sums, and canonical this and canonical that, which I ploughed my way through to some understanding of - I think. The thing that got me, though, was keeping track of all the Greek letters. I'd be following some proof nicely, and then get confused, then realise that I was mixing up this symbol with that (none of them had names to me; they were purely visual symbols - nameless visual symbols - apart from the occasional pi or alpha or beta, etc.). Obviously the slow progress was down to more than just the symbols getting confused in my head, but that looked like something easier I could detour to, and get out of the way as an obstacle in a fairly no-brainer kind of way, and off I went. Never came back. Got into the Greek alphabet, and then the Greek philosophy book, which had some Greek writing in it, and then maybe something else tangential to getting familiar with those symbols, and then life happened or something, and the algebra book became something that was there "for later". (I might've even found out that I was getting beyond myself, and that this was the main reason for the confusions. Oh, and I also started formally studying, so that took priority, too.) How to get the Greek alphabet uploaded? Well I don't even now have the whole thing uploaded, so I'm probably the wrong person to talk to as far as that goes, but as far as individual symbols go, one way of getting familiar with them (without that familiarization being a distraction from the maths you're doing) is to either write "Greek English" with them, or find Greek words containing them that aren't too hard to remember. Give them a context. I think that applies to mathematical symbols, too. Give them a context. There aren't that many purely mathematical symbols, and a lot of them have been created to "contain their own context". Turn A upside down, to get for-All, turn E upside down to get Exists, stretch a skinny s into a snake shape for an integral (which is a "sum"), or use a Greek capital S to write S-for-Sum. Most of those, though, you remember just by using them often enough. No need to go outside of maths to find ways of using them. Another thing that helps is to sometimes just practice writing symbols as nicely as you can, trying to speed that up, repeating, like you're learning to write all over again - which is what you're actually doing. Learn to write the way you learnt to write the first time you learnt this. It sounds like soul-destroying repetition, but it's something you can do while thinking of something else more interesting. Good way of making your inner voice just shut up a while for a time, too. Sometimes that's exactly what you need - stillness.

[@mathcritic]

Edward Scheinerman's Mathematical Notation.

[@netinhonaruto10]

How to understand algorithm calculations from thomas cormen's introduction to algorithms book? Do you recommend a book or tutorial?

[@jimcognito4631]

The fact that you play magic is too perfect. Let me guess you play izzet combo or like Dimir?

[@Maths_3.1415]

Excellent books 👍👍

[@vicocovi7327]

Muy interesante hechicero

[@O46185O]

💚 That’s a really cool book!! 💚

[@boogerie]

I think even more basic and more to the question would be studying set theory and predicate logic. There are books on these topics from the University of Calgary's Open Logic Project which has books on these subjects for download for free. Followed by Schaum's Set Theory, While we're on the subject of proof writing, how could you forget Hammack's BOOK OF PROOF?

[@prod.kashkari3075]

Hey math sorcerer. I’m a senior in college and I’m a statistics major and math minor. I’ve taken classes that overlap with math majors, such as 3 semesters of calculus, differential equations, 2 semester of linear algebra, and 2 semesters of real analysis. But I have not taking 2 semesters of abstract algebra. Do you think it would be hard for me to get into a Math Masters program? I haven’t taken abstract algebra, so I feel like I’m not a strong candidate for MS math programs, compared to say for MS statistics programs.

[@matt566]

Alright Math Sorcerer MTG Arena stream when?

[@sverrirjensson9772]

Other books on proof reading would be A Logical Introduction to Proof by Daniel .W.Cunningham I have read it and it´s a great book and first two chapters deals only with logic first one with some propositional logic and the second with predicate logic then the next chapters are on proof strategies and diagrams,mathematical induction and set theory final chapters are then on proofs in abstract algebra and real analysis.One other book to mention although it hardly on mathematical proofs is An Introduction to Formal Logic by Peter Smith an excellent introduction to the subject.It begin arguments and what is an argument ? and what is a valid argument? From there it goes deeper into propositional logic using truth trees and then into Quantifiers that to say into predicate Logic and ends with extensionality and Identity.The first book require no more than high school mathematics and the second doesn´t require any mathematical background.

[@adamodimattia]

Dibs on equal 500.000 subscribers noted!

[@mediccjh2948]

Where didjya get those coasters?

[@acdude5266]

The problem comes with technical papers, where it seems that authors make their own symbols,

[@sukd2669]

that green book is very expensive

[@Maths_3.1415]

Congrats for (5×10^5) subscribers :)

[@TheMathSorcerer]

Thank you!!!!!!!

[@childintime6453]

Do you own "Principia Mathematica" by Russell and Whitehead?

[@TheMathSorcerer]

yes I do!

[@childintime6453]

@@TheMathSorcerer It would be great if you make a video about it in the future. Love your channel

[@VulcanGunner]

it is another language, with no errors allowed.

[@coffeeconfessor4747]

I feel like math is a language in which science speaks. Symbology in math can be super confusing. But with physics, math symbology can be backwards.. (I'm staring at you polar coordinates!)

[@tonie1048]

Is it possible to have a complete understanding of everything in math

[@30803080308030803081]

No, math is too big now. Maybe that was possible in the 19th Century.

[@aikidograndmaster1781]

Every thing in Math is easier said than done ...if you want to learn anything in Math, you better have loads of free time , the best books and or/ instructors and last but not least talent...

[@a0z9]

El cero es la mujer y el 1 el hombre. Los demás son sus hijos.

[@monsterclass]

🫠

[@godsofwar1186]

Please help me Obiwan Kenobi you are my only hope. Planks constant reduced ℏ looks exactly like the astronomical symbol of Saturn. Why is my question?

[@douglasstrother6584]

Max Planck: "He Blinded Me With Science!" (with apologies to Thomas Dolby)

[@monsieurLDN]

What are you doing

[@OrdenJust]

en.wikipedia.org/wiki/ISO_31-11

[@OrdenJust]

Oops. Superseded. ISO/IEC 80000