As an aerospace engineer, i have all those books too. I keep them on the shelf as a grim reminder of all the starry eyed dreamer friends i lost along the way.
But they're an inspiration to the next generation, like my daughter, who wants to go into the AE field, like you have. My son is heading more towards a CJ/JD route, but then he's only four, so he might change his mind. ;-)
I received my B.A. and M.S. in math over 50 years ago. After working in private industry for a few decades I taught math at the community college level from 2000 to 2020. Now that I'm retired I can speak freely. I've observed that the publishing of elementary math textbooks (elementary meaning everything up to and including calculus) is a shameless racket. Every year they come out with new editions that are sold at outrageous prices and are not improvements of previous editions and of course students are always expected to buy the newest edition. In 1968 I bought the 4th edition of Thomas' Calculus for $19.95 and used it for three semesters. It covers more material than current editions that cost over $200 and best of all it has the answers to all the problems, not just the odd-numbered ones, so it is ideal for self study. My advice to anybody interested in learning math is to hunt thru used book stores for texts that are at least 30 years old.
Sometimes I beat myself up about not being a perfect student, especially with coronavirus and online learning now, thinking I'm gonna have to settle for a fast food career, so it's really reassuring to hear you in one scene talk about having to drop a course cause it's too hard, and in the next scene talk about teaching math in college.
Maybe I will change my major after watching this video. I am currently a Math Major as a non-traditional older student. I am also a disabled veteran. So far I am doing pretty good in college. My GPA is just over 3.9, but I am just a part-time student. Older non-traditional student. Believe it or not I am 68-years-old. I'll be 69 in August. As a disabled veteran, I have had to deal with traumatic brain injuries (TBI). It does cause short term memory problems at times. As long as my grades stay above 3.0, I will continue on as a Math Major.
As a highschooler this was very helpful and insightful. Currently I'm at the end of sophomore year but I've already completed my school's AP AB calc course at the top of the relatively small class (I would have gone for BC if they had it). Next year I'll be taking AP stats at the highschool and they won't have anything left for me come senior year. As a student math is the subject I would never want to stagnate in even for a month or two. I'm having to take part time college classes to avoid it by next year. This definitely helps out for deciding which direction and order I should move in math. My academic/intellectual life goal is to learn, understand, and fully or nearly fully comprehend all branches of mathematics I could have access to.
You know you're a math person when you have multiple books on a subject, e.g. more than one calc book, more than one LA book, more than one DiffEQ book. Much of my personal library is math, languages, physics, chems, bio, biochem, crafting, music, cooking, and baking. And it's dwarfed by my sister's larger-than-some-public-libraries collections on a broader range of scholastic and non-scholastic topics. Slide rules. Abacuses. Cards. Dice. You name it. All a tiny fraction of my world, but one in which I choose to show my children. And my daughter LOVES math! It's her favorite subject, and she's in second grade!
I absolutely loved Friedberg’s Linear Algebra, I used it for self study for a first course in Linear Algebra and I remember having so much fun with it. I found it incredibly intuitive and challenging, the proofs become progressively more complex so I never really struggled with any. Furthermore, together with Herstein’s Abstract Algebra these were by far the books that prepared the most for, and made me good at, proof writing which later made my study of Analysis very enjoyable and easy going. An excellent recommendation for anyone wanting to learn what Linear Algebra is really about.
I was thinking about learning linear algebra as my preparation for a uni before i finish highschool. Thx for recommendation, I was struggling to find a good literature on internet.
To see books in video above, just click on time in blue highlight. Please correct me if I made any error below. 0:29 Calculus by James Stewart 1:23 Physics for Scientists and Engineers by Serway Jewett 2:13 Modern Physics by Paul A Tiplex and Ralph A Llewllyn 2:35 Logic and Proof by Norman, Sherwood and Bar 3:00 A Introduction to Abstract Mathematics by Robert J Bond and William J. keane 3:26 Mathematical Statistics with Applications by Dennis D Wackerly, William Mendenhall III, Richard L. Scheaffer 4:50 Fundamentals of Differential Equations and Boundary Value Problems by Nagle, Saff and Snider 5:32 Discrete Combinatorial Mathematics by Ralph P. Grimaldi and Frank L. Salemann 6:25 Elementary Linear Algebra and Matrices by Richard M. Caron and Frank L. Salemann 7:22 Linear Algebra by Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Sphence 8:26 Partial Differential Equations, An Introduction by Walter A. Strauss 8:55 Fundamentals of Complex Analysis by E. B. Saff and A. D. Snider 10:20 Abstract Algebra, A First Course by Dan Saracino 10:58 Advanced Calculus, A Couse in Mathematical Analysis by Patrick M Fitzpatrick 11:59 Elements of Point Set Topology by John D. Baum.
I'm impressed you took a physics specialized book as a math major but also surprised no real/numerical analysis, number theory, differential geometry or any kind of geometry classes?
Edit: just finished watching the video and at least Real Analysis was covered in the "Advanced Calculus" course (the one in which Fitzpatrick book was used, shown in vey end). Still intrigued about Numerical Analysis and Number Theory though Well observed! I've always thought Real Analysis was an essential course for a mathematician, but it seems not be the case. I imagine, in their curriculum, the topics usually covered in Real Analysis must have been covered in the Complex Analysis and Topology courses, with nothing really being left out, while the proof skills must have been included in the second Linear Algebra course
I know this is old but I find it odd too- I teach HS maths and they recently took geometry out of our highest level maths course... not sure why. Maybe some international conspiracy against geometry haha. Just thought it was an interesting coincidence.
I just took numerical analysis 1 in this semester and real analysis in the last. I think I took differential geometry in my sophomore year. I think I'm about to take numerical analysis 2 and number theory in my next semester. Also, I think probability is something that is a must for Math majors as well, which he sorta left out in this video.
It would be great to see a perfectionalized version, that is, a set of best books (according to you) for a close to perfect curriculum. How would you put together a full math major reading list?
@@TheMathSorcerer Actually, euclid's books are the second most studied books in the world. The most studied being the bible. thought that might be interesting.
Decisions, decisions: Yes, doing nothing is an option, but there are other elder care options for calculus texts: 1) have the book rebound by a local or regional printing firm, 2) remove the cover boards, punch binder holes in the pages, and store them in a three (ore more) ring binder, perhaps with a zip-to-close cover, 3) divide the book into per-chapter segments, and store them in manila folders together with worked solutions in adjacent manila folders in hanging folders in a filing cabinet, 4) recognize the image of Darth Vader's helmet in the cover, then erect a cremation pyre, and hold a math friends funeral party to dance around the burning pyre while chanting and singing. (Watching Star Wars 4-5-6 in advance is recommended.) Alternatively, one could donate the item to a local book pound, and adopt a newer, younger book with similar material as a companion for a longer life.
I love these videos where you go through a stack or shelf of mathematics books. So many I haven't known about and it is great to get introduced to them.
The engineers had a leg up on you in the complex numbers class. EEs use complex numbers/analysis by the end of their sophomore year in circuit analysis. The material on the first test was probably a review of work they had already done in their engineering courses.
@@TheMathSorcerer Complex numbers are why EE majors like DC more than AC. It's also why one of my profs a decade ago had to recommend a specific calculator model. Turns out the list of calculators that can solve a system of linear equations containing complex numbers while not having programmability or onboard storage is quite short.
Thanks!!! This helps me a lot, I can’t afford(time) to start an undergraduate degree in mathematics but I’m definitely willing to learn by myself. This will be a great guide. Cheers!
William Keane, who wrote Intro to Abstract Mathematics, was my professor for that class at Boston College. I was lucky enough to take the last class he taught 2 years ago before he retired. Funny thing is, he didn't require his students to get his textbook, and he actually said it would be somewhat of a waste of money because he wrote class notes. He even told me that if I really wanted to get it, I could probably find it floating around online somewhere for free!
I’m a meteorology major and so many people don’t realize how much of a math and physics intense field atmospheric science is. You essentially are applying the laws of physics and math to the atmosphere. Very interesting!
I took topology before doing multivariable calculus, and I think it was absolutely the right move. Topology might have been a bit easier to do after or at the same time as, but multivariable calculus is so hard on its own that any advantage is well worth it.
Is multivariable calculus really that hard? I honestly don't remember; but my course was a loooooong time ago. I don't remember it being especially hard; it just seemed like an obvious extension of single-variable calculus. But that could just be faulty memory.
I love this pile of math books. Mine was very similar. The day I walked into my schools graduate math library and saw rows and rows and rows of math books did I realize my math degree education was nothing but a whiff of the subject. I was sampling a drop from a vast ocean created before my time. Humbling!
I used Linear Algebra Done Right (Axler), Advanced Linear Algebra (Roman) and if you want to do proofs the easy way then use Serge Langs Linear Algebra and have fun with determinants. sheldon axler provides his book free online.
awesome! i'm in 7th grade and i'd love to take physics and chemistry, these book's is indeed interesting to read! (i'm doing an advance learning btw :))
If you get through Calc 3, Physics becomes a trivial class. You'll love it even more, and that'll lead you to Chem, Orgo, and eventually PChem and BioChem (w/Bio on the way).
Take this book if you like advance stuff, quantum field theory and advance topics of condense matter, have fun, I had this courses this semester and this is some cool stuff to learn, I'm a physics major specialized in superconductors
"This is the class that makes math majors reconsider their major" this hit home. I honestly only passed because of a curve. I remember going into to the final and answered 0.75/10 questions. First question was a "recite the definition of a partition" and I basically just froze there and wasted about an hour staring at my page. Had another question where I probably just wrote down "By the Bolzano-Weirestrass theorem, this is true"
I’m in the last year of my math degree and I’ve taken most of these classes, but because of my actuarial science minor I’ve taken a math course on interest theory, one on financial derivatives, and one on actuarial models instead of topology, complex analysis, and discrete math. But yea I completely agree with you on how difficult the mathematical statistics and real analysis sequences are, by far the hardest classes I’ve taken
I study math in the Czech republic, so I thought I’d just explain how our curriculum works, for comparison. The standard bachelor’s program is called general mathematics, but technically only the first two years are general, in the third year students choose courses based on what master’s program they want to pursue. We rarely use textbooks, most of the material is provided by the lecturer. First year: Discrete mathematics, Linear algebra 1 and 2, Real analysis 1 and 2, Programming 1 and 2, and one more course out of a number of options (I chose a physics course). Second year: Algebra 1 and 2, Real analysis 3 and 4, Measure theory, Numerical mathematics, Geometry, Introduction to probability and mathematical statistics. Third year: Complex analysis (only course mandatory for everyone) I wanted to do master’s in probability or statistics, so my third year also included the following: Probability theory 1, Mathematical statistics 1 and 2, Stochastic processes 1, Mathematics in finance, Introduction to optimization, Functional analysis, Analysis of matrix calculations We also have a mandatory swimming exam, mandatory English exam and four semesters of mandatory sports classes.
@@raymondxiao2716 Indeed. We have to slowly and rigorously define and prove calculus before we actually get to use it. It's considered the hardest class in the first two semesters.
I've used the same book for a complex analysis course, the last math course I've taken and the only one I've gotten a D in. The course was not required for math majors. I'd also taken: - multivariable calculus (required for both math B.S. and B.A., A, textbook: Calculus, Multivariable: Early Transcendental Functions by Smith & Minton) - intro to differential equations (required for both math B.S. and B.A., A, textbook: An Introduction to Differential Equations and Their Applications by Farlow) - intro to linear algebra (required for both math B.S. and B.A., A, textbook: Linear Algebra and Its Applications by Lay) - discrete structures (not required but recommended as a prerequisite to analysis i, A, textbook: forgot) - intro to mathematical analysis i (required for both math B.S. and B.A., C, textbook: Introduction to Real Analysis by Bartle & Sherbert) - intro to partial differential equations (not required, B, textbook: Solution Techniques for Elementary Partial Differential Equations by Constanda) - intro to mathematical analysis ii (required for math B.S., B, textbook: Elementary Classical Analysis by Marsden & Hoffman) - intro to modern algebra & number theory (not required, C, textbook: Abstract Algebra by Beachy & Blair) - intro to probability theory (not required, B, textbook: Introduction to Mathematical Statistics by Hogg, Craig, & McKean) - geometry (not required, C, textbook: forgot) - intro to mathematical statistics (not required, A, textbook: same as the one for probability) - linear algebra (not required, B, textbook: Linear Algebra Done Right by Axler) I've also taken many physics courses because until my last year of university I was a math & physics double major: - intro physics i (required for math B.S. and for both physics major and minor, C, textbook: forgot) - honors intro physics ii (required for math B.S. and for both physics major and minor, A, textbook: forgot) - intro physics laboratory (required for physics major, B) - intro physics iii (required for both physics major and minor, C, textbook: Vibrations and Waves by French) - intro to computational physics (required for physics major, B) - modern physics (required for physics major, B, textbook: forgot) - thermal & statistical physics (required for physics major, B, textbook: An Introduction to Thermal Physics by Schroeder) - electromagnetic theory (required for physics major, A, textbook: Introduction to Electrodynamics by Griffiths) - electronics for scientists (required for physics major, C, textbook: forgot) - intermediate mechanics (required for physics major, C, textbook: Classical Mechanics by Taylor) - optics laboratory (required for physics major, C) - relativistic physics (not required, C, textbook: Gravity: An Introduction to Einstein's General Relativity by Hartle)
Hi Math Sorcerer, I’ve been following/ watching your videos. I realized solid geometry/ mensuration topics books was never discussed. It may be good subject to discuss geometry books nowadays does not go in depth in this subject. Solid Mensuration by Kells, Kern and Bland is a well known obsolete book might be a good addition to your collection to discuss.
I lived off campus in a house that was closer than the dorms to the math building. The landlord was Dr. Edward Pease and he wrote the Calculus text I used for Cal I,II and III. First semester freshman year it was a new book just written and published. I supplemented it with Schaum's Outlines. Plenty of questions in it. Back in '67 no digital devices. I lived every minute of math in HS, college and grad school.
I feel cheated, all those books are less than what I had to read in a single course in my major. We were asked to read 1000 pages every single week per course, so at the end of the semester, we had to give an exam on around 60,000 pages. The hardest exam I took was a final oral exam that took about 6 hours, the required reading list for that course was about 8 pages long, so it took me an entire summer reading 18 hours every single day to sit for that exam, I put every book on top of each other as I finished reading them and at the end that pile was bigger than me (from the floor almost to the ceiling of my room). I did get an A+ on that exam, but they asked about every single book on that list and, when the list was over, they continued with books that weren't on the list (which I was lucky to have read as well since I do a lot of research beyond what is expected on any course).
GOD real analysis. I aced it but only because my prof was absurdly generous with grading. I took it literally two semesters ago, much of the class failed because they copy-pasted answers on the take home final off of Chegg and their copy-pasted answers were incorrect.
@@zapazap I think it is very class dependent. I really liked my proofs class for the same reason you describe, but my real analysis felt like a lot of memorization (it is entirely possible I am biased here, though - I really prefer studying discrete math and it has been my focus whenever I have been able to choose a focus).
Seeing that Mathematical Statistics Book gave me cold shivers. I'm taking a course in Mathematical Statistics and Data Analysis this year, and it makes me want to cry.
That you so much for this. This is exactly what I need. Out of college for a few years and I have some free time so I'm going to self study the math right. Once Im done I'm planning to dive into string theory. My biggest regret of collage was real analysis always conflicted with some core physics class so I couldn't double. I always knew I really needed to for theory.
I am at UMD where Fitzpatrick teaches (I opted for a different professor for scheduling reasons.). Naturally, we use his book for real analysis. It's a great resource---packed to the gills with material---but definitely not the "gentlest" of introductions to the topic. Let's just say the on-ramp is short and he jumps into the calculus quicker than some other texts. For a more thorough treatment of the fundamentals and other prerequisite knowledge, I like Tao's Analysis I & II or Abbott's Understanding Analysis.
Great vid! I used Purcell's for Calculus and it's a pretty decent book for me. Btw in my uni, i need to take geometry classes (Analytical Geometry, Transformational Geometry) and i struggle the most at it
It amazes me how much math there is. It is immense! Probably just as much depth and complexity as say physics and chemistry. You have covered some very esoteric topics in the past. Combinatorics, topology, and other stuff like that. What are your thoughts on differential geometry and tensor calculus?
@@TheMathSorcerer That would be pretty cool if you did. Do you know the applications of combinatorics? It just seemed to me like one of those esoteric topics like onomatology(the study of names.) edit: If this is not too personal, what exactly do you do for a living?
Its very likely to be deeper than the depths of physics and chemistry. Physics etc. Have a hard time with infinities. As for Math, well you see ..... ♾
@@starshipx1282 Well Putin my fellow comrade, Math definitely is very dense and deep. Like philosophy. Which makes sense. Math is a branch of philosophy called epistemology, which is the branch of philosophy dealing with how we acquire knowledge.
10:20 same here. Abstract algebra was thé best class I've taken. At first, i thought thé best class I'd taken was calculus (probably because i loved Prof Herbert Gross's lecture séries available here on youtube) Then I thought, "no, linear algebra is thé best!" Again, probably because of some online lectures I found on LA by Prof. Gilbert Strang. Now, i think abstract algebra is the best.
I studied topology before I took my first real analysis course. The grader of that course hated me! (I would do my assignments in terms of 'open covering's and the like.)
@@TheMathSorcerer : He eventually stopped grading my assignments. I did them anyway and just kept them. Showed them to my prof at the end of term. He just glanced through them and counted them all good. :) He was an excellent prof -- one of my favourites. He was (East) Indian and listened to Indian classical music. Playing some for me he said 'What she is doing is creating a continuous function with her voice'.
Hey man I love your videos, would you consider make a video similar to this one, taking a bunch of popular majors like physics, economics, engineering, etc and listing the math classes that those majors take, please? Kind of the other side of the coin.
Great video! I think have never understood Jordan composition, so it's sad that the Caron & Salzmann textbook is out of print. Would you recommend another one please?
So, what science classes do you take so you have a Bachelors of Science? Most of the folks doing the math degree with a secondary education minor took physics as their science, because most of physics, is just calculus.
O my! It took me way more math classes and thus going over more math books than what you have to get my BS in pure math. Those are just half of the math books I have. 🤯
I wasn't required to take statistics, which looking back was unfortunate. I also took topology early, I think I got a C, but it did help prepare me for the class on Real Analysis.
At National Taiwan University, in the Calc I for the math majors, the math department uses Taiji Takagi's A Course on Analysis as the textbook, with Courant and John's Introduction to Calculus and Analysis I and II, and Protter and Morrey's A First Course in Real Analysis for references. By the end of the first week, the professor introduced the Fundamental Theorem of Calculus and derived the anti-derivatives of polynomials. Couple weeks later he introduced the metric space and the Heine-Borel Theorem. Already you can tell that they're taking a holistic approach to mathematics. BTW, for a pure math degree, a curriculum with no mathematical logic is questionable, with no set theory is unbelievable.
generally not a good idea to compare math majors in Asia to those in the US lol. You could become a math major in the US without taking super rigorous courses imo.
I think there were a lot of books missing. A lot of geometry was missing. Analytic geometry in 2D and 3D. Euclidean / synthethic geometry. Projective geometry, neutral geometry, non-euclidean geometry. Differential geometry. Also some metric-space topology, axiomatic set theory, logic and categories was missing.
There's a choice here in subsidiaries, like five of them. Physics and statistics are most recommended but there's chemistry, economics, geology and geography. I took geography and physics. For physics I had physics by Halliday, both volumes.
I don’t see any geometry besides topology, not even differential geometry! Do you think that geometry is neglected for a lot of math programs? I believe my program only has pure math majors take differential geometry.
Can't find Elementary Linear Algebra and Matrices by Caron anywhere. Not only can't find the book on any store, but I can't even find a mention of it anywhere online (though it may just be drowned out because there are so many linear algebra books). Bit of a disappointment after it was given such a glowing recommendation.
Would be cool to see a Discrete Maths showdown and your opinions on Rosen vs Grimaldi vs Epp. This is somewhat of a debate in CS on which textbook is the better one for discrete maths
Hated physics with all my soul. I failed physics 2 during my second semester, had to retake it during summer and thank god I got the minimum passing grade.
Yeah that's the way it works at my school too. I took chemistry 1 and 2 for my science credit but in hindsight I probably should've taken physics since I feel it's more "mathy" than chemistry is. Still was fun though! It's important for a math geek to know a little about the other stem fields.
At my college yes they have two take two physic courses UAlbany University. My majors are Political science and history. But I have a friend that majored in Math.
Do you read the whole book or just the stuff you need (for example some topic you didn't understand or some topic you want to get better understanding of)? My seniors are suggesting only to read books when I have some problem understanding some topic in lectures. I'm in my first year btw.
Yup that's good advice, because you have to manage your time. If you have time to read extra stuff, do it, but usually you are hyperfocused on your classes since you have to do well in those.
