[HN Gopher] Everything you always wanted to know about mathemati...
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Everything you always wanted to know about mathematics (2013) [pdf]
Author : ggr2342
Score : 622 points
Date : 2023-05-25 12:22 UTC (10 hours ago)
(HTM) web link (www.math.cmu.edu)
(TXT) w3m dump (www.math.cmu.edu)
| [deleted]
| optbuild wrote:
| A finely written book for beginners. I like how it slowly
| explains stuff rather than doing in Theorem Proof style short
| books.
| billfruit wrote:
| Does it cover geometry?
| fn-mote wrote:
| No, as a quick perusal of the table of contents would tell
| you.
|
| For geometry, get a book like Art of Problem Solving's
| Introduction to Geometry. That will cover many beautiful
| topics in a question and answer style.
|
| [1] https://artofproblemsolving.com/store/book/intro-geometry
| layer8 wrote:
| I wish there were such books for more advanced math topics.
| SleekEagle wrote:
| I wish math had its version of Griffiths
| tr33house wrote:
| is there a service that can print, bind and mail PDFs with as
| many pages as this? It'll be useful for some of the manuals I
| have to read too
| vishnugupta wrote:
| I use this site [1] and can recommend them. Though I don't know
| if they are available outside of India.
|
| [1] https://www.printonweb.in
| 01100011 wrote:
| I used Barnes and Noble Press a couple years ago to print a
| book. Cost $25 or so and was impressed with the results.
| tesin wrote:
| A quick google turned up this service -
| https://www.printme1.com/
| ohwellhere wrote:
| $47 for this work via that service
| phkx wrote:
| There might be a print shop in your area which offers similar
| services. Or services which explicitly offer to print thesis,
| but they typically require a minimum number of prints.
| emacdona wrote:
| https://www.lulu.com/
|
| I used lulu.com to print a copy of OnLisp [1]
|
| What I got was one of the best bound paperback books I've ever
| held.
|
| <rant> I wish all publishers would just sell eBooks (and
| publish settings like "optimal paper size") so that I could
| print my own copy using a service like lulu. One of my biggest
| gripes with hardcopy books nowadays is that the paper stock
| they use is so thin that the ink on the other side of the page
| shows through. Lulu let's you choose the paper stock. I really
| can't say enough about how happy I was with the quality of the
| printed book lulu sent me. </rant>
|
| [1] https://www.lurklurk.org/onlisp/onlisp.html
| BeetleB wrote:
| There are a lot of variables.
|
| I print them myself and take them to FedEx to do the binding.
| Letter size/A4, though, result in big books and a lot of paper.
| So I wrote a script that produces a new PDF and reorders the
| pages. In the new PDF, you have two pages per side of paper (4
| pages per sheet). The reordering is done so that FedEx can cut
| the sheet right in the middle, and put the left half on top of
| the right half to get the usual ordering. Then they just bind
| it.
|
| Not counting the cost of my paper, they charge about $11
| (probably can get it a bit cheaper but I add some extras in the
| service when I bind them).
| Frummy wrote:
| Perhaps use the pdf split function to order 4 quarters of the
| pdf in separate binds
| mindcrime wrote:
| In another recent thread, somebody mentioned using some Amazon
| feature for doing this. I might be wrong, but I _think_ you
| sign up as an author, upload the PDF like it 's your book, then
| buy one copy (or request a proof) for yourself, and then delete
| it. Maybe somebody who has used this facility can chime in with
| more (or better) details...
| actinium226 wrote:
| If I could read, and understand, a textbook like this in a day, I
| would be so happy. Alas, I must only look with longing at the
| links provided by HN, thinking wistfully 'someday...'
| rg111 wrote:
| The key to learning Math in adult life, as I have found-
| setting aside 40-180 mintues every day to learn regularly.
|
| It would be golden if you can create a study group that meets
| weekly. Just start a discord/Element room/Zulip/IRC chat and go
| from there.
|
| I am learning Topology as an adult and learned Category Theory
| this way.
|
| This truly works.
|
| Setting aside time 4-5 days a week works. Make it a habit.
| ConnorMooneyhan wrote:
| As someone with a B.S. in Pure Mathematics who is now a
| programmer, it makes my heart happy to see my true love at the
| top of HN.
| [deleted]
| ggr2342 wrote:
| Did you use it at CMU?
| ConnorMooneyhan wrote:
| No, I actually didn't use this book. By "true love" I meant
| mathematics ;)
| pmoriarty wrote:
| One thing I've always wanted is a comprehensive guide to
| mathematical notation, which tells you what symbols mean or at
| least what field of mathematics they come from.
|
| I frequently come across all sorts of weird mathematical symbols
| in papers, and of course these symbols are virtually never
| explained, so I have no idea what they mean.
|
| Even better would be if there was some way an LLM could read
| through a paper itself and then explain the equations.
| SleekEagle wrote:
| many books will have a page in the preface that lays out the
| notation, even for very common objects. it's hard to make a
| cheat sheet for something like this because many symbols are
| used in different fields, and even if different subfields of
| the same field.
| cubefox wrote:
| I think that's pretty rare?
| ivan_ah wrote:
| RE: math symbols
|
| Check out this excerpt of definitions of basic math notation I
| use in my books:
| https://minireference.com/static/excerpts/set_notation.pdf It
| has some examples of the "alien symbols" [?] (for all), [?]
| (there exists), etc.
|
| One problem (feature?) of math notation is that paper authors
| don't follow a consistent convention for symbols, so what
| you're asking might not even be possible... It doesn't help
| that different math domains might use different symbols for the
| same concept! That being said, there is the ISO 80000-2
| standard that defines recommendations for many of the math
| symbols, with mentions of other variations, see
| https://web.archive.org/web/20210705180417/https://people.en...
| You might want to read through that as a starting point.
|
| Unfortunately, just knowing the notation (being able to read
| the symbols) is not usually enough. Understanding each
| symbol/concept usually requires knowing the math context and
| other related definitions of the domain where the notation is
| used. In other words, knowing the notation is not a shortcut
| for learning math... But still, I hear you about the need to
| select some symbols then right-click and choose "read this to
| me" or "explain this to me."
| cubefox wrote:
| One thing I love about programmers is that they rarely use
| complex symbols. They are the complete opposite to
| mathematicians in this regard. Basically all programming
| languages consist just of ASCII keywords. So when in doubt
| about some keyword, you can just use Google and type it in.
| Together with the name of the language.
|
| I guess symbols look fancier and are more concise.
|
| Also, mathematicians do love their PDFs. No doubt because it
| supports their beloved symbols so well. Of course PDFs are
| terrible for the Web and screens in general, but only a
| programmer would care about _that._
| sorokod wrote:
| I doubt that having a "dictionary" attached to a math paper,
| something like
|
| 1. [?] = nabla see https://mathworld.wolfram.com/Nabla.html
|
| 2. ...
|
| 3. ...
|
| would improve your understanding. Notation encodes ideas, it is
| the understanding of the ideas that is tricky, not the
| encoding.
| pmoriarty wrote:
| It would actually help. I'd know what fields I need to study
| to more fully understand the papers I'm interested in.
|
| It would also help me figure out what to ask LLMs (or people)
| to explain to me.
| cubefox wrote:
| GPT-4 can probably explain LaTeX formulas pretty well, but
| when they are compiled PDFs, the encoded PDF plain text is
| often garbage, so GPT-4 probably couldn't understand much.
| dwheeler wrote:
| If you want to go deeply into formalized mathematics, take a look
| at the Metamath Proof Explorer
| <https://us.metamath.org/mpeuni/mmset.html>. It defines a set of
| axioms, and formally verifies every proof showing every step
| (hiding nothing).
| zhte415 wrote:
| To echo others on writing style, it's very lucid. This would be a
| fantastic coffee table book; not for everyone, but for a
| countable number of people.
| utopcell wrote:
| what group of people is uncountable ?
| slopbop wrote:
| If I remember correctly, Brendan Sullivan had a reputation as a
| TA for Concepts of Mathematics at CMU as "Math Jesus", not sure
| if that was a testament to his pedagogical skills or just due to
| the long hair and beard...
| ggr2342 wrote:
| Where is he now? Why doesn't he write more books like this? I
| mean in this lucid explanatory style.
| foobarbecue wrote:
| "This work is submitted in partial fulfillment of the
| requirements for the degree of Doctor of Arts in Mathematical
| Sciences."
|
| So does that mean this is his PhD thesis? What's a Doctor of
| Arts?
| shwestrick wrote:
| It's a doctoral degree with a heavy emphasis on pedagogy and
| teaching. From https://www.cmu.edu/math/grad/phd/index.html:
|
| > The Doctor of Arts degree shares all requirements and
| standards with the Ph.D., except with regard to the thesis. The
| D.A. thesis is not expected to display the sort of original
| research required for a Ph.D. thesis, but rather to demonstrate
| an ability to organize, understand, and present mathematical
| ideas in a scholarly way, usually with sufficient innovation
| and worth to produce a publishable work. Whenever practical,
| the department provides D.A. candidates with the opportunity to
| use materials developed to teach a course. While a typical
| Ph.D. recipient will seek a position that has a substantial
| research component, the D.A. recipient will usually seek a
| position where research is not central.
| hapidjus wrote:
| https://en.wikipedia.org/wiki/Doctor_of_Arts
| witchesindublin wrote:
| I like how the book is written in a teaching style rather than a
| textbook style.
| uldo wrote:
| Beautifull! Is there similar book on physics?
| Koshkin wrote:
| Susskind's series does a pretty decent job walking the reader
| through topics in (theoretical) physics. At a somewhat more
| advanced level, you can try Schwichtenberg's No-Nonsense books.
| I also enjoyed Stevens' The Six Core Theories of Modern
| Physics.
| ivan_ah wrote:
| Do you mean basic physics like mechanics (PHYS 101) ? If this
| is what you're interested, check out my MATH & PHYS book.
| Posted link to it in another comment this thread.
| abhayhegde wrote:
| I'd say the Feynman Lectures of Physics [1] volumes cover a
| broad base with some topics in great detail as well.
|
| [1]: https://www.feynmanlectures.caltech.edu/
| rg111 wrote:
| No.
|
| Feynman Lectures, to be properly understood requires one to
| be at least an advanced undergrad.
|
| Most people just use it as home decor and many use it like a
| novel.
|
| To _properly_ appreciate the material, you need training in
| Physics. Otherwise you will be getting much less.
| dexter89_kp3 wrote:
| this is awesome
| 1equalsequals1 wrote:
| https://pimbook.org/ Read this instead
| Koshkin wrote:
| Read both.
| fn-mote wrote:
| That book has a completely different focus... breadth instead
| of understanding argumentation.
|
| I agree that the Programmer's Introduction to Mathematics is
| more likely to contain useful content (instead of being about
| how to develop the ability to reason carefully). It also has a
| LOT more breadth than the OP.
|
| The free part of Chapter 3 "On Pace and Patience" is a key very
| important attitude toward learning from this book (especially
| on your own). If you are thinking about studying from this
| book, make sure you philosophically agree.
|
| I tried to copy and paste a paragraph here, but it looks like
| it has been ROT-13 encoded in the PDF (or something)!
|
| > [...] mathematical culture requires being comfortable being
| almost continuously in a state of little to no understanding
| It's a humble life [...]
| zdms wrote:
| Its using ROT25 -\\_(tsu)_/-
| anthk wrote:
| It looks a lot like Gentle Introduction to the Art of
| Mathematics.
| no_wizard wrote:
| Does anyone know of an entry level book that could take someone
| through say, high school math to college alegbra / calculus?
|
| This is my singular biggest hurdle in going back to school to
| finish my degree and I'd love to fill the gaps I have around
| mathematics so I can not only finish my degree; I'd also like to
| participate in some more advanced computer science that rely
| heavily on underlying computation.
| steppi wrote:
| It's not one book, but for everything before calculus it would
| be difficult to beat the books in Israel Gelfand's High School
| Mathematics Correspondence Curriculum [0]. These are designed
| for self study and give a fresh perspective on topics they
| cover.
|
| [0] https://www.goodreads.com/series/318605-gelfand-
| corresponden...
| wyclif wrote:
| Excellent recommendation; they are very good books to start
| with. Concepts are clearly explained and I wish every
| mathematics textbook was structured like this. Some people
| are biased against these books because they're Soviet, but I
| find that attitude parochial. If we're judging textbooks on
| their merits alone, these will get you to Calculus.
| rg111 wrote:
| For this partcular purpose, look no further thank Khan Academy.
|
| I recommended a lot of people these courses and myself went
| over a few videos to revise Trigonometry.
|
| I can vouch for the quality.
| dataviz1000 wrote:
| Curious if I could find another interesting way to learn math
| for someone who hasn't gone to college, I asked chatGPT to
| cluster 20 animal emojis by taxonomy and use them to explain
| Affinity Propagation like I'm 5 year old. (I'm an idiot.) More
| or less, the lion emoji wants to be friends with the tiger
| emoji more than the dog emoji with some explanation of the math
| and math symbols in between.
|
| ``` For example, when Scar wanted to be king, he sent a
| "responsibility" message to the other big cats, trying to
| convince them that he should be the leader. However, the
| "availability" message he received back was weak because most
| animals didn't trust him.
|
| Meanwhile, Simba sent out a strong "responsibility" message
| showing he could be a good leader, and in return, he got a
| strong "availability" message back with many animals showing
| support. That's why Simba was a better leader for the Pride
| Lands, according to Affinity Propagation!
|
| ```
| nemexis wrote:
| I absolutely adore the works of John Bird:
| https://www.google.com/search?tbo=p&tbm=bks&q=inauthor:%22Jo...
|
| it really takes you from the ground up all the way to advanced
| subjects. He published multiple books on various levels of
| mathematics.
| ajmurmann wrote:
| I love this book: https://www.goodreads.com/book/show/17406856
|
| The explanations are great and the examples and excises are
| such that you can just do them in your head.
| ivan_ah wrote:
| I think you might like my book "No Bullshit Guide to Math &
| Physics"[1,2,3], which contains a condensed review of high
| school math (a.k.a. algebra and precalculus), then explains
| PHYS and CALC topics in an integrated manner.
|
| [1] website https://minireference.com/ [2] PDF preview and
| sample chapter =
| https://minireference.com/static/excerpts/noBSmathphys_v5_pr...
| [3] concept map =
| https://minireference.com/static/conceptmaps/math_and_physic...
|
| If you prefer something focussed on a review of high school
| math topic, then you might prefer the "green book" instead, see
| https://nobsmath.com/
| jayro wrote:
| At Math Academy (https://mathacademy.com), we created a series
| of courses, Mathematical Foundations I, II, & III, that will
| take a student from basic arithmetic through calculus and
| prepare them for university-level courses like Linear Algebra,
| Multivariable Calculus, Probability & Statistics, etc. You can
| jump in at any with an adaptive diagnostic that will custom fit
| the course to you based on your individual strengths and
| weaknesses.
|
| https://mathacademy.com/courses/mathematical-foundations-i
| https://mathacademy.com/courses/mathematical-foundations-ii
| https://mathacademy.com/courses/mathematical-foundations-iii
|
| We also have courses on Linear Algebra and Mathematics for
| Machine Learning:
|
| https://mathacademy.com/courses/linear-algebra
| https://mathacademy.com/courses/mathematics-for-machine-lear...
|
| It's not free, but our adaptive, AI-driven algorithms makes it
| the most efficient way to learn math that you're going to find.
| We've had numerous students master 3-5 years of math in a
| single year.
|
| We're still in beta and haven't done a proper Show HN yet, but
| we're getting there!
|
| I'm the founder, so I'd be happy to answer any questions.
| pmoriarty wrote:
| _> our adaptive, AI-driven algorithms makes it the most
| efficient way to learn math that you 're going to find_
|
| Can you elaborate on this? What do these algorithms do?
| jayro wrote:
| Geez, I'm trying to figure out how to describe in a short
| paragraph or two what it would take a book to explain.
| Here's my best shot.
|
| We've created an extensive knowledge graph representing all
| of mathematics (3,000 topics and counting) from 4th Grade
| Math up through our university-level material, and our
| algorithms traverse the graph to identify the optimal
| learning tasks to assign to the the student at any point
| based on their performance on previously completed learning
| tasks: diagnostics, lessons, reviews, quizzes, etc.
|
| There are actually multiple graphs, including one that
| defines the direct prerequisite relationships between
| topics as well as one that describes encompassing
| relationships (e.g. the topic on Solving Two-step Linear
| Equations fully encompasses the topic on Solving One-step
| Linear Equations Using Multiplication), but there are other
| graphs as well.
|
| In addition, the algorithms have to deal with spaced
| repetition, which is vastly more complicated to sort out
| within the context of a hierarchical knowledge structure
| with both full and partial encompassings. (Without
| encompassing relationships, the backlog of reviews would
| quickly slow progress to a crawl).
|
| We actually have some deep-dive writeup in the works that
| attempt to explain how all of this works at a level that
| will be accessible to most people, but it's more than I can
| describe here, unfortunately.
|
| Anyway, I hope this helps a little.
| no_wizard wrote:
| When I am ready to dive into this again, I will definitely
| look at this. I know I need concrete time dedicated to this
| sort of thing (repetition is the only way to master it
| really) but I'll circle back around to this soon!
| Gerard0 wrote:
| Looks great and was ready to sign up but I surely wasn't
| expecting that price! I am not saying it is not worth that,
| but as someone who has tried to start learning math on my own
| only to quit afterwards for whatever reason, it's a big risk
| to take.
| Math-Ninja wrote:
| Hi Gerard.
|
| Math Academy does not charge your card for the first 30
| days. If you find it's not a good fit for then you can
| cancel within this period and you won't be charged. 30 days
| hopefully gives you enough time to determine whether it's a
| good fit or not.
| admsmz wrote:
| I've been a paying customer since October last year. I
| discovered it after someone recommended it in a hackernews
| comment.
|
| I'm guessing you're mentally comparing this to all the
| possible books you could buy instead for that price. But
| how many of those books would you actually read, let alone
| finish? A better comparison is, having an MIT educated math
| tutor on call for $50 a month.
|
| I have a bachelors in physics but it still feels great to
| learn new things that my education skipped. For example, we
| skipped singular value decomposition at my university in
| the interest of time. Mathacademy says, screw it, we're
| teaching everything!
| jayro wrote:
| I guess you have to think about it like this.
|
| How much would it be worth to you to learn 3-5 years of
| math in a single year without getting stuck? And I mean
| really learning it to the point where you're able to solve
| the more difficult problems and are not merely able to
| recognize some of the symbols and terminology and talk like
| you know it. If you're just kind of curious about some
| advanced math topics you see pop up on HN from time to time
| and aren't really willing to invest any real time, effort
| or money into learning the material, which is totally fine
| and is probably where most people reading this comment are,
| then sure, spending more than $40 on a book or watching
| some free online videos will seem expensive.
|
| But the reality is that very few people will be able to
| learn a significant amount of math by simply working
| through some problems in a book. Eventually they'll get
| stuck or just run out of gas, and when I say eventually I
| mean probably in 2-3 weeks. But if you're that one student
| who successfully taught themselves multiple courses worth
| of mathematics on their own from a few books and outside of
| any educational institution, then hats off to you! You're
| like that guy who put on 30 pounds of muscle doing pushups
| and pull-ups at the local park. You know, ... that ONE guy.
| ;)
|
| But if you want a sure fire way of mastering a large amount
| of mathematics as efficiently and painlessly as possible,
| then you want a system like Math Academy that will adapt to
| your individual learning curve and knowledge frontier and
| push you through the material using the most effective
| pedagogy available - careful scaffolding, active problem-
| based learning, spaced repetition, gamification, etc.
|
| The bottom line is this. Our system is more effective than
| any course available and is much cheaper for what you get.
| In fact, we just had a group of students ages 11-13) start
| with basic pre-algebra in the fall of 2021 (as in Solve x -
| 4 = 10) and from what I've heard all did extremely well on
| the AP Calculus BC exam a couple weeks ago. That's like 6-7
| academic years of math in 18 months and we're expecting
| mostly if not all of them to earn a 5 (the top score).
|
| But take my word it. Try it out for yourself. You
| automatically get a full refund if you cancel in the first
| 30 days, so there's no risk. And we're always available to
| answer your questions and support your progress.
| rodneyzeng wrote:
| I did not see any content related to number theory and
| combinatorics (or counting) in the list of courses.
| jayro wrote:
| We should have those courses ready within the next year.
| Multivariable Calculus should be available in another few
| weeks, then Probability & Statistics at the end of July,
| then Methods of Proof, followed by Discrete Math, and
| Abstract Algebra later this fall. But courses in Number
| Theory, Graph Theory, Combinatorics, Real Analysis, etc.
| are all planned.
| graycat wrote:
| Very fast calculus: Consider a standard car with a speedometer
| (reports how fast are going) and an odometer (reports how far
| have gone).
|
| Easily enough we can take the speedometer readings, say, 1 time
| each second, and calculate a good approximation to the odometer
| readings. That is a 1 second approximation to the calculus
| operation of _integration_.
|
| Similarly we can take the odometer readings, say, 1 time each
| second, and calculate a good approximation to the speedometer
| readings. That is a 1 second approximation to the calculus
| operation of _differentiation_.
|
| If we use smaller time intervals than just 1 second, then we
| will usually get a more accurate approximation. It is a theorem
| that, under mild assumptions, as we let the lengths of the time
| intervals shrink toward 0, the results of the operations will
| reach limits and quit changing.
|
| Those limiting values are the actual definitions of
| differentiation and integration.
|
| No big surprise, under mild assumptions, if we start with the
| odometer readings, differentiate to get the speedometer
| readings, and integrate to get back the odometer readings, then
| we really will get back the odometer readings. That is the
| fundamental theorem of calculus.
|
| Some common mild assumptions are basically that the speedometer
| readings change only continuously (no jumps) over time and we
| are working over only finitely long time intervals.
|
| Newton's second law of motion
|
| force = mass x acceleration
|
| essentially guarantees the continuity of the speedometer
| readings and, thus, justifies the integration back to the
| odometer readings.
|
| Of course, calculus and Newton's second law of motion are close
| cousins in both theory and applications -- no big surprise
| since Newton essentially created both (might mention Leibniz
| and some others).
|
| Can quickly show that if we integrate time t, we get (1/2)t^2.
| So if we differentiate (1/2)t^2 we will get back t.
|
| A calculus course will show how to differentiate and integrate
| a wide variety of mathematical expressions, polynomials, sines
| and cosines, products, quotients, _composite_ expressions,
| etc.. E.g., differentiate sine(t) and get cosine(t).
| Differentiate cosine(t) and get -sine(t). Can also find many
| cases of arc lengths, areas, volumes.
|
| Suppose we are starting a business. At time t, let the revenue
| be y(t). Suppose we have argued that as we reach all our target
| customers, our monthly revenue will be b. Suppose we argue that
| due to word of mouth advertising the rate of growth is
| proportional to both the number of happy customers talking and
| the number of target customers not yet customers listening.
| Denote the rate of growth of y(t), that is the derivative, by
| y'(t). Then for some constant of proportionality we should have
|
| y'(t) = k y(t) ( b - y(t) )
|
| Of course we know current revenue, say, at time t = 0, that is,
| y(0).
|
| Then by the first weeks of calculus, can show that, with TeX
| syntax,
|
| y(t) = { y(0) b e^{bkt} \over y(0) \big ( e^{bkt} - 1 \big ) +
| b }
|
| More generally
|
| y'(t) = k y(t) ( b - y(t) )
|
| is an example of an _initial value problem of a first order,
| linear, ordinary differential equation_ and an introduction to
| a course in ordinary differential equations.
|
| Calculus has wide applications to physical science,
| engineering, economics, finance, spread of diseases, etc.
| engineer_22 wrote:
| Check out Kahn Academy, they have a gamified course to guide
| you through the equivalent of a high school and early college
| math curriculum. AFAIK it's free?
| culi wrote:
| Khan Academy is great. When I was taking AP calculus in
| highschool I failed to complete any homework and barely
| passed the class. But when it came time for the AP test I
| binged Khan Academy videos for 3 days beforehand and ended up
| getting a 5 (the max score). Great resource and even
| bingeable
| alphameese wrote:
| Specifically these three courses [0][1][2] will take you from
| basic algebra to precalc. They're very thorough and I've
| found them extremely useful in upgrading my high school level
| math skills. I have heard that their calculus courses aren't
| sufficient though, and that it should be learned from
| somewhere else.
|
| [0]https://www.khanacademy.org/math/math1
| [1]https://www.khanacademy.org/math/math2
| [2]https://www.khanacademy.org/math/math3
| bloemheuvel1 wrote:
| Would you recommend this path over doing the Algebra 1 ->
| Geometry -> Algebra 2 .... etc path?
| alphameese wrote:
| The Math 1-3 courses intersperse all of those courses and
| provide a more streamlined path. I would personally
| recommend using those 3 courses to learn up to pre-calc.
| engineer_22 wrote:
| https://www.khanacademy.org/math
| diebeforei485 wrote:
| I found this to be a good explanation of Calculus in
| particular: http://lightandmatter.com/fund/
|
| It assumes you have some algebra, but does not require college
| algebra.
| quickthrower2 wrote:
| Interesting! No touch on probability/stats though? Or calculus?
| fn-mote wrote:
| This is a book about writing proofs.
|
| It is intended to develop that skill, not introduce you to a
| breadth of topics.
| mbork_pl wrote:
| Well, there's too much of (modern) mathematics to touch
| everything - even everything important... One of the most
| important notions is that of _compact sets_ , and it's not even
| mentioned. Neither are groups (well, they _are_ mentioned, but
| not much else), etc.
|
| From a quick skim of the ToC this looks very well thought-out.
| Looks like an excellent book!
| billfruit wrote:
| Does it touch geometry?
| bannedbybros wrote:
| [dead]
| nailer wrote:
| Slightly off topic - does anyone know a 'reader mode' for PDFs?
|
| I frequently look at PDFs online and am looking for a tool that
| reformats the PDF into a single column, so I can just scroll,
| absorbing the content.
| adamgordonbell wrote:
| At some point I was interested in learning to read and write
| proofs.
|
| I did the "Introduction to Mathematical Thinking" MOOC from Keith
| Devlin. The curriculum is available as a book as well.
|
| The class is basically how to write and read proofs for non-math
| majors. It starts pretty slow, but gets harder at some point. The
| number theory proofs were fun.
|
| You 'got to' grade others proofs online, and they graded yours
| which was an interesting way to get familiar with reading and
| writing proofs.
|
| I recommend it because instead of an area of math it focuses on
| what it means to prove something. And the teacher is pretty
| entertaining.
|
| https://www.amazon.ca/Introduction-Mathematical-Thinking-Kei...
|
| https://www.coursera.org/learn/mathematical-thinking
| lmwnshn wrote:
| Judging by the URL, this book was used for CMU's 15-151 / 21-128,
| which is a first-semester course for CS and math undergrads.
| Nowadays, the course uses [0].
|
| [0] https://infinitedescent.xyz/
| rgrmrts wrote:
| I remember using Mathematical Thinking [0] for Concepts of
| Mathematics (21-128) which is also a great book!
|
| [0]
| https://www.goodreads.com/book/show/445059.Mathematical_Thin...
| temp51723 wrote:
| That book was used in my "intro to higher math" class my
| freshman year. A very humbling experience, seeing that cover
| again gave me a bit of a knot in my stomach.
| lawrenceyan wrote:
| https://infinitedescent.xyz/dl/infdesc.pdf
| roter wrote:
| Thanks for this resource. It also serves as a LaTeX math
| example --- the source for the book is provided.
| rickstanley wrote:
| Does this replace the OP? Or is "An Infinite Descent into Pure
| Mathematics" a complementary book?
| lmwnshn wrote:
| My link replaces; we did not use OP's book when I took the
| course.
|
| That said, OP's book looks more conversational in tone, which
| I personally have a slight preference for.
| lying4fun wrote:
| Every chapter of the OP book has an introduction which has
| the following subchapters: Objectives, Segue from previous
| chapter, Motivation, Goals and Warnings for the Reader. Which
| I really appreciate and I think its a great way to teach
| stuff, especially mathematics, since all those chapters
| contextualize the coming topic in various ways. (E.g. I
| imagine 'Motivation' does this with respect to the history
| and origins of the idea and 'Segue from previous chapters'
| contextualizes it with reference to the stuff reader has
| learnt so far. I didn't read anything yet but it looks
| promising
| mmmmpancakes wrote:
| fancy name for what seems like a fairly standard "intro to
| proofs" textbook, at least based on the ToC.
| RedPanda250 wrote:
| Can someone share how this compares to Math for Computer Science
| by Lehman, Leighton, and Meyer ?
| https://courses.csail.mit.edu/6.042/spring17/mcs.pdf
| Alifatisk wrote:
| I love the style, I'll download it when I get home. Is there
| anything similar but for statistics?
| rubergly wrote:
| Came here to ask the same question. Really hope there are some
| good recommendations!
| cubefox wrote:
| If you search this post for "statistics", you find several
| recommendations (over similar books):
|
| https://www.lesswrong.com/posts/xg3hXCYQPJkwHyik2/the-
| best-t...
| cubefox wrote:
| Note that these are 700 pages which could take multiple years (if
| you're doing it in your spare time) to go through. I'm not sure
| who would have the motivation and discipline for this.
| l33t233372 wrote:
| It might, but it shouldn't. There are 8 chapters and most of
| the content in the first 7 shows up in any run of the mill
| "Introduction to Higher Mathematics" or whatever that
| university decides to call their first actual math class,
| although occasionally combinatorics will replace number theory
| content.
| abhayhegde wrote:
| Most of the books are meant to be consumed in parts. This book
| explicitly mentions "Segue from previous chapter" for most
| chapters indicating what key concepts are continued in
| exploring/building new ones. Also, I believe any reader on HN
| can make sense quickly of the basic definitions needed to
| understand a concept in isolation.
|
| However, mathematics is especially known to require continuous
| dedication for years to attain any sort of mastery.
| eimrine wrote:
| Kids, cherry-picking students of other disciplines, those who
| really understand what is a good read.
| Koshkin wrote:
| > Everything you... wanted
|
| Far from being "everything" anyone would want or need, it's
| rather "some (fundamental) things" you _must_ know. A couple of
| pages a day, on average, would get you there within one year.
| cubefox wrote:
| Still, I'm in doubt that a significant proportion of us would
| have the discipline for this. One reason why some things are
| pretty much only learned in university is that they provide
| the necessary motivation.
| shae wrote:
| I collect interesting problems and learn the math that can
| solve them. I do best by directly connecting fun and
| learning.
| shanusmagnus wrote:
| I've been very interested in this method for a while. How
| do you find the math that would solve them? Is it well-
| understood, or is it easy to figure out in practice?
| Would love to hear more about how this looks for you
| practically.
| BeetleB wrote:
| It depends on how rigorous/detailed you want to be. This is at
| most two semesters worth of material, and has a very shallow
| learning curve (hence the large PDF). If you've been exposed to
| these ideas, you could cover it in a semester. I'd say it's
| quite doable in a year in your spare time.
|
| If you drop the combinatorics chapter, it is definitely doable
| in one semester.
|
| For example, Chapter 7 is 100 pages. In Tao's analysis book, he
| covers the same material in 42 pages.
| evanmoran wrote:
| As a CS major who went to CMU years ago, my favorite book from
| all of my professors was for my 15-213 class called Computer
| Systems: A Programmers Perspective
|
| I remember at the time the book was in loose leaf paper so it
| warms my heart to see the book has a 3rd edition. It was used as
| a core part of teaching assembly, memory representations, and
| getting students ready for the operating systems class. When I
| help people learn to program, it's the only book I think is a
| must have:
|
| https://www.amazon.com/Computer-Systems-Programmers-Perspect...
| wbrd wrote:
| Going through this now and it's great
| GitPushOrigin wrote:
| Is there a book or resource you'd recommend for operating
| systems? I recently finished CS:APP and really enjoyed it.
| Though I've been programming for ~7 years and felt that made it
| easier to digest.
| BanazirGalbasi wrote:
| We used this for my Computer Architecture class in college and
| it's one of the few textbooks that I wish I had kept around. I
| had a used copy so not selling/returning it to the bookstore
| really wouldn't have been too impactful at the time. Now that
| I'm wanting to get back into low-level programming, I miss it
| even more.
| rg111 wrote:
| > it's one of the few textbooks that I wish I had kept around
|
| What are the other books that keep around or wish to keep
| around?
| donkey-hotei wrote:
| +1. This book changed my life. Wouldn't be doing what I'm doing
| today without it!
| istjohn wrote:
| This looks great! Does anyone know of any solution sets for the
| exercises or other resources with similar problem sets with
| solutions?
| hgsgm wrote:
| Art of Problem Solving website and books.
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