[HN Gopher] Paul's Online Math Notes
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Paul's Online Math Notes
Author : happy-go-lucky
Score : 288 points
Date : 2020-11-13 11:46 UTC (11 hours ago)
(HTM) web link (tutorial.math.lamar.edu)
(TXT) w3m dump (tutorial.math.lamar.edu)
| Schoolmeister wrote:
| Great stuff. Well witten notes with clear and extensive examples.
| I actually used this just a few months ago to pass my calculus
| exam. Feel like I learnt a lot more than from my overly dense and
| formal textbook.
| erdaniels wrote:
| This got me right through Calculus II :)
| paulpauper wrote:
| This is a great resource. The notes should be printed up and used
| for textbooks instead of those huge, overpriced books
| colmvp wrote:
| The thing I appreciated the most when I was self-learning math
| was the answers where he explained the steps cogently, which was
| incredibly helpful in seeing where I went off the rails or got
| stuck.
| spike021 wrote:
| In college I used a mix of these and PatrickJMT's videos on
| Youtube.
|
| The awesome thing about Patrick's YT channel is that he walks
| through a plethora of examples for all kinds of concepts. So if
| you're more of a hands-on learner who doesn't absorb as much when
| your instructor just lectures without showing/demonstrating a
| concept, then the channel is a great supplementary tool.
|
| I wouldn't have made it to my degree in CS without his content.
| albrewer wrote:
| Dr. Dawkins was my calc. 2, 3, and differential equations
| professor when I went to school for engineering.
|
| He's an absolute treasure as far as teaching goes, and I don't
| think I'd be as successful and skillful at math had I not had him
| as my instructor. He's insanely energetic and positive in the
| classroom, and he's basically perfected the art of getting "math"
| into other people's heads.
| mechanicalDigit wrote:
| Never thought I would see another Lamar grad here.
| PTOB wrote:
| Same here. How many of us are there?
| bachmeier wrote:
| I've never been to Lamar, so maybe you know something I
| don't, but there's no sense in which Lamar is a small
| school. It's probably several times the average US
| university.
| mechanicalDigit wrote:
| My computer science cohort was very small. That's why I
| don't expect to see many Lamar folks on these types of
| forums.
| cs2818 wrote:
| There are dozens of us! I took Cal 2 and 3 from him.
| virtuous_signal wrote:
| It's amazing to think how much welfare a single person's free
| work can add to the world. Basically FOSS but for learning math.
| I used this site ~12 years ago when taking calculus courses, and
| more recently I put it as a recommended resource on my syllabi
| when teaching those same courses. Apparently many others
| benefitted as well. A gift for exposition + selflessness + a
| permanent domain name (I'm guessing, due to his job at a
| university) = profit for everyone.
| aardvarkr wrote:
| I had the honor of being a student of his. I was a high school
| student while attending college there thanks to a Texas program
| for gifted kids. As a professor he's quite the character with
| his beard and his rat tail and his funny mannerisms. If you
| think his online notes are good, well, his lectures were an
| order of magnitude better those of than any other calculus
| class I've been part of. I wish he would make them available
| online.
| ntsplnkv2 wrote:
| Honestly it's like a rite of passage to use Paul's notes to get
| through calculus in college :).
|
| Many thanks because without it I would've struggled much more!
| bigasscoffee wrote:
| been around for awhile, I used these for Calc 2 in 2008, and
| linear algebra and doffeq in 2010/11!
| mirrorlake wrote:
| When I graduated college, I e-mailed him a thank you note for all
| the help his site gave me. It truly is a great resource.
| mkl95 wrote:
| Classic! I used to read these before I dropped out of Physics to
| make software for a living.
| matthewh806 wrote:
| I could write this exact sentence out and it still be true :D
|
| Seriously, a great collection of notes. These were easily the
| most well written, thought out, understandable & digestible
| notes I ever came across during my studies.
|
| Blows most textbooks and professors out of the water
| isatty wrote:
| Never thought I'd see this here. I started studying Calculus I
| from here before I started university. It's really amazing how
| well structured and written these notes are. No video lectures
| needed to understand.
|
| I didn't attend a single lecture for Calc I and II in school and
| still did okay all thanks to this professor.
| albrewer wrote:
| When he teaches in person, he literally reads these notes and
| writes them on the board. He revises his notes based on
| questions he gets in class when something doesn't click for
| students. He's been teaching for over 20 years now so they're
| very polished at this point.
| nsriv wrote:
| Piling on to the praise here, but I cannot explain how much this
| site has helped me go from a C+ high school math student failing
| my first year of college calculus, to majoring in statistics, and
| now being a math teacher myself. Truly one of the best resources
| on the internet.
| driscoll42 wrote:
| Seconding many here, I used these 10+ years ago in my Calc, Diff
| Eq, and Linear Algebra classes. Far superior to many of the texts
| I had to work with. So glad people are still getting value out of
| it. I remember checking a couple years ago expecting it to be
| taken down for some reason and happy to be wrong.
| Hasz wrote:
| For math outside of calculus, I highly recommend Wolfram
| MathWorld. Good definitions, reasonably concise, and the primary
| sources are listed.
|
| https://mathworld.wolfram.com/
| paulpauper wrote:
| that is way too broad. mathworld does not give many examples
| mhh__ wrote:
| Mathworld is good to search for relatively wacky stuff (As is
| Wikipedia - you can sometimes find niche results squirrelled
| away in the depths of a big article), but as a resource for
| learning it's not great.
|
| It is true that outside of Calculus (through to real and
| complex analysis) and Linear Algebra the density of good
| teaching material online decreases
| disabled wrote:
| This is effectively the best reference notes on the internet for
| calculus 1, calculus 2, calculus 3, and differential equations.
| You can definitely become proficient in these subjects on those
| notes alone, with practice. Paul's Online Math Notes were my main
| reference material back in 2008-2009 in university. I am glad to
| see that it is still very popular.
|
| The absolute best Calculus book for undergraduates majored in the
| formal engineering disciplines is Calculus, 6th edition, by
| Swokowski, Olinick, and Pence.
|
| ISBN-10: 0534936245 ISBN-13: 978-0534936242
|
| My (fraternal) twin brother used this book to teach himself
| calculus 2 in preparation for another course he needed to take.
| There are lots of supplementary materials that you can get for
| the book, like solutions manuals, study guides, and even a linear
| algebra supplement (although the latter is hard to find--I should
| probably scan all of the materials)
| robviren wrote:
| 10/10, would have not made it through diff EQ without this site.
| Had to self teach because of constant professor changes. So lucky
| I found this site in 2012.
| aliljet wrote:
| Funny seeing this here, but a decade ago, this professor's
| differential equations explanations saved me from endlessly
| meandering through tough engineering lectures and dense math
| textbooks. I'm frankly curious to know if undergraduates and high
| school students still use this...
| techwizrd wrote:
| I used this when I took differential equations while working on
| my math major (graduated in 2016). It's simply invaluable for
| the anxious, confused student.
| [deleted]
| sq_ wrote:
| Can confirm that they do. At least at the schools I've been at,
| "Paul's Online Math Notes" is an instantly recognizable name
| for most STEM students.
| gibspaulding wrote:
| I graduated in '17 and used his site a ton once I got to
| classes beyond what Khan academy offered. It's an excellent
| resource!
| CaptP wrote:
| High school student here who self-studied multivariable
| calculus and differential equations. I absolutely LOVE Paul's
| Online Math Notes.
| MisterBiggs wrote:
| In the last year of my Aerospace Engineering degree. This site
| got me through calculus and I still use it any time a
| differential equation shows up in my studies since they still
| scare me.
| pcbro141 wrote:
| I just graduated university this year and used the site in high
| school and a little bit in university (just freshman year
| calculus). I don't remember how I found the site, either I was
| Googling math stuff, or a friend was and sent me a link. Many
| friends in high school and university used the site, it's
| definitely still popular. A high school teacher may have
| recommended it as well. It's a great site.
| ppur wrote:
| In high school right now; my calc teacher links to this all the
| time when the textbook's explanation/examples are
| unsatisfactory
| paulpauper wrote:
| why are differential equations so difficult? it would seem even
| smart people struggle with understanding them. Is the problem
| is how they are taught or is the concept inherently hard/ It
| should not be that hard given that we're taking 'rates of
| change' broadly speaking, yet it is.
| peterwoerner wrote:
| Both. They are taught, generally speaking, by giving a series
| of techniques to solve problems without the underlying
| mathematics (i.e why those techniques work on those
| problems). Calculus generally takes some time to grok, which
| typically doesn't have unless your really into it. Think how
| many people fail to grasp exponential growth (the simplest
| ODE).
| reedf1 wrote:
| The concept of a differential equation is not hard. Solving
| differential equations can range from trivial to non-trivial.
| mhh__ wrote:
| Good scientists are often terrible teachers.
|
| That and people default to being scared of mathematics rather
| than seeing difficulty as proof of it being rewarding to
| learn.
| legerdemain wrote:
| Even among the engineering-oriented lower division math
| courses, material in differential equations courses is both
| antiquated and presented like a laundry list. This essay is
| more than 20 years old now, but the complaints are basically
| as relevant today.[1]
|
| [1] https://web.williams.edu/Mathematics/lg5/Rota.pdf
| sartaj wrote:
| Good source
| programmertote wrote:
| I wish I could donate something to keep this site up and running.
| Really admire people who spent their time creating a useful
| resource like this and sharing it for FREE with the public for
| common good. I hope I will have free time one day (when I retire)
| to do something like that for the subject that I'm interested in.
| gongo1 wrote:
| Incredible source of material for Calc 1-3
| KingEllis wrote:
| Speaking as someone ashamed at having never taken Calculus, I
| didn't know there were 3 of them...
| albrewer wrote:
| First you learn basic calculus. Then you learn advanced
| calculus. Then you learn how to apply what you've learned to
| more than one dimension. The second one is actually the
| hardest of the three.
| gpanders wrote:
| In my experience:
|
| Calculus 1 = differential calculus
|
| Calculus 2 = integral calculus and infinite series
|
| Calculus 3 = multivariate calculus
| gibspaulding wrote:
| Calculus 1 = regular calculus
|
| Calculus 2 = backward calculus
|
| Calculus 3 = n dimensional calculus
|
| Differential Equations = inside out calculus
|
| Complex Analysis = imaginary calculus
| AlanYx wrote:
| Don't forget: Real Analysis = generalizable calculus
|
| That was my favorite course.
| Drblessing wrote:
| This website helped me so much!
| maccard wrote:
| This site was more useful to me than EUR300 of textbooks during
| my undergrad. I had to purchase two books so I could submit the
| homework, and in all honesty, I learned nothing from them, very
| little from the lectures. Almost all of my library algebra and at
| least my first 4 calc courses we're handled by Paul (and khan
| academy occasionally)
| uptheroots wrote:
| This is an amazing resource! Used it in college a lot
| Scarbutt wrote:
| Sequences, Probability and Counting Theory seems like a rare
| omission.
| therein wrote:
| While I realize I am just repeating the sentiment that others
| have already shared, I would like to do so in case Paul sees this
| and realizes how many people he has helped.
|
| Best content online about Calc I, II, III and DiffEq. Hands down.
| siraben wrote:
| Never thought I'd see Paul's Notes on the front of HN. My
| classmates and I used it so often when we learned calculus in
| high school, and it still is useful at the university level for
| multivariable, vector calculus and differential equations. Huge
| kudos to Paul.
| lordnacho wrote:
| Great notes. Now my question is whether there's some sort of
| standard for what's in Calc 1, 2, 3...
|
| I've seen a number of people on the internet refer to them, but
| it doesn't seem clear to me what the numbers mean. Wouldn't this
| be different depending on where you were? And yet people talk
| casually about the numbers instead of the topics (first order
| diff eqs).
|
| I'm European, did my degree in the UK, and never came across any
| standardized numbering.
| throwaway2245 wrote:
| I have tutored people taking Calc 1, 2 and 3 at several
| universities in the US.
|
| There's no exact standard that I'm aware of, but they tend to
| closely align at different universities. Dividing James
| Stewart's Calculus into three parts is a reasonable guide: you
| can see the contents on Amazon preview.
|
| I'd expect solving first order linear differential equations
| would be solidly in Calc 2.
|
| * https://www.amazon.co.uk/Calculus-Transcendentals-
| Internatio...
| mlamat wrote:
| When I studied Calculus 1 Khan Academy didn't exist yet and I had
| no one to turn to for tutoring. I fell into a depression and
| wasted at least a year of my life.
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