
Paul's Online Math Notes - rfreytag
http://tutorial.math.lamar.edu/
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Pingviini
I highly recommend Professor Leonard's videos to anyone struggling with
Calculus.

[https://www.youtube.com/user/professorleonard57](https://www.youtube.com/user/professorleonard57)

I must also confess that his ability in helping me understand and fall in love
with Calculus two years ago was the main impetus for me to select Mathematics
as my major. I'm now focusing my attention on Number Theory with high hopes of
one day becoming a Theoretical Mathematician.

I should also add that Princeton Companion book to Mathematics is a valuable
resource for learning what is out there in Pure Mathematics.

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wrong_variable
> 'Theoretical Mathematician'

what does that even mean ?

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todd8
My first degree was in "Theoretical Math". I took classes in subjects like
Number Theory, Topology, Analysis, Non-commutative Ring Theory. The subjects
were about Math not how to do Math to solve other problems. We studied proofs
not applying math to solve word problems.

As an example, I wasn't very good at solving differential equations, a very
important part of math used to solve many real-life problems. Instead I
studied things like the Lebesgue Integration which extends the notion of
integration to a larger set of functions for which the more familiar Riemann
integral wouldn't be defined. That was taught in my second semester real
analysis course that had these prerequisites: Real Analysis I, Complex
Analysis I, Differential Equations, Calc I and Calc II. A lot of work to get
to an interesting subject, but a subject of interest to Mathematicians not
engineers using math. An undergraduate degree in Applied math, in contrast to
theoretical math, would probably have involved learning more about, say,
differential equations.

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wbhart
Usually this is called pure mathematics, as opposed to applied mathematics.

On the other hand, applied mathematics might also involve some pretty
technical "theoretical maths", which though being applied, can be studied for
its own interest without the application.

So in some sense, "applied maths" sometimes means maths that is applied,
rather than maths that can be applied. For that reason it perhaps makes sense
to instead use the term "theoretical maths", though I am not sure if that is
standard terminology or not.

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tekproxy
I had this guy as my math teacher. He was an absolute machine. Always came in
at exactly the same time, put his bag down, took his watch off, and started
transmitting knowledge. Loved his classes.

All homework problems were really realistic with messy answers and the test
questions were easy. Only a few problems for both.

Once, when talking about higher dimensional math, a student asked if string
theory said there are 13 dimensions. He quickly replied "yeah" and I'm sure he
knew it was more complicated than that but it was an irrelevant question.
Without thinking I blurted out it was _consistent_ with up to 13 dimensions
and the whole class turned around to look at this kid who corrected The
Machine. He quickly admitted that was true and moved on. Highlight of my
education.

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rfreytag
Taken from this Reddit thread with many other fine mathematics resources:
[https://www.reddit.com/r/AskReddit/comments/4e6cim/what_is_t...](https://www.reddit.com/r/AskReddit/comments/4e6cim/what_is_the_best_free_way_to_catch_up_on_advanced/)

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JamilD
After three years so far of undergraduate engineering, very few days go by
where I don't have this site open in at least one tab!

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Zombieball
Paul's notes got me through many of my engineering courses as well (+4 years
ago).

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tarheeljason
Really nice, succinct notes here as well:
[https://www.math.hmc.edu/calculus/tutorials/](https://www.math.hmc.edu/calculus/tutorials/)

(includes some linear algebra, despite the URL)

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kaitai
Yep. One benefit of the HMC notes over Paul's is that the HMC notes have more
visualizations. I thought the linear algebra portion of the HMC notes (change
of basis, eigenstuff) was especially useful for learners as a counterpoint to
most textbook presentations.

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nimos
Maybe a sign I should get back to studying calc.....

Another resource is
[https://www.youtube.com/user/patrickJMT/](https://www.youtube.com/user/patrickJMT/)

Khan Academy is good if you don't know anything but I like PatrickJMT's videos
better if you're reviewing.

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jammett
Good to see this site still alive, I used it back in 2006 and I got
distinctions thanks to the site.

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ageofwant
Very good. Every so often I get despondent about the state of the world; then
I'm reminded that somewhere some bright Indian girl is figuring out how to
build a fusion reactor from pigshit and string with knowledge she gained from
sites like this. One can hope.

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sna1l
This is how I made it through all of college. This man is a god.

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IndianAstronaut
Another good online math resource.

[http://faculty.atu.edu/mfinan/nnotes.html](http://faculty.atu.edu/mfinan/nnotes.html)

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joeyrobert
This got me through undergraduate calculus I, II, III and differential
equations. Can't recommend it enough, it's a free text book. One of those
hidden gems you can occasionally find on professor's websites.

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avianbc
Thanks to these and patrickJMT on youtube, I was able to ace all my college
math courses.

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marpstar
After passing Calculus I with a C in college about 8-9 years ago, I found this
site and started working with his examples. I ended up passing Calculus II
(regarded at the "hardest" math class at my college) with a B+.

Highly recommended!

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bthornbury
These are the best online math notes around. I used them as a textbook
replacement for many math classes in college (from Diff EQ to Triple
Integrals) and never had a time where it didn't cover something I needed.

Really great resource here.

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medymed
Fantastic resource for learning and as a quick reference. Coincidentally was
browsing it before I stumbled upon this post.

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krob
I didn't take Eigen Values & Vectors until I took Linear Algebra. In his notes
he went over Eigen Values in Diff Eq. Not Vectors, but rather functions. Also
I never learned Fourier Series in Diff Eq. We did go over Laplace
transformations. Where ever he took this material, they were insanely
thorough.

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markwaldron
Paul's Math Notes got me through all of my undergrad math courses. My
professor was fantastic, but having these to reference when the professor
wasn't around was a much-needed asset to learning and finishing homework. I
recommend this site to everyone I know taking Calculus or higher courses.

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vzip
He used to have Linear Algebra material as well. I wonder why he took it down.

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Someone
Those cheat sheets baffle me. I cannot imagine that someone who needs help
remembering, to pick a few examples, that

    
    
       a^m a^n = a^(m+n)
    

or that

    
    
       y = mx + b
    

is a line will be able to use those facts in a real-world problem, with the
cheat sheet in hand.

For those who used these and found them useful: did you really use them as
cheat sheets, that is, to look up things while working on a problem, or did
you use them more as a checklist before entering an exam, to check that you
remembered most of them?

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kaitai
I suggest big parts of Paul's Online Notes to students who need some brush-up
or remediation. When I was teaching college precalc, for instance, people
usually had a reasonable grasp of y=mx+b but difficulties with exponentiation
were almost universal. Some of these "cheat sheets" are useful for such
students just to tape above their workspace so that while working through the
rote mechanical practice problems they must do they can use the "cheat sheet"
as a checklist while they work.

The review of complex numbers, on the other hand (not a cheat sheet but a
condensed review) I assign to some masters' students who have not used complex
numbers for 2 years and need to recall what they once learned. There it's just
a concise but reasonably comprehensive refresher list.

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Someone
That makes waaay more sense to me; the first uses them more as training wheels
than as cheat sheet; the second is more akin to the "check that I know it"
that I envisioned. Thanks.

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bradlys
Yep, love this guy. His notes helped me through my calculus finals in high
school eight years ago and then through college as well.

If you notice an error be sure to correct it though. I did once while studying
for my high school finals while staying up to 3AM. He responded quickly and
fixed it immediately. Great to see someone who pays attention.

Just checked my email account. Apparently, I've emailed him corrections three
times over the period of 4 years. He always emailed back within 24 hours.

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amjaeger
This site is how I learned calculus & the only reason I never failed a math
class. But I wish he had some notes for linear algebra

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kaitai
He did have linear algebra notes at one time but took them down, I believe.
Agreed -- I'd love to have those!

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sillyquiet
I had Prof. Dawkins for Calculus a good decade and a half ago. He was a
fantastic teacher, and the reason I finally 'got' a lot of the concepts I had
struggled with up to then.

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zxcvvcxz
Great notes, I remember using these years ago for calculus and differential
equations. Very straight-forward and example-based. Remember for most of us
math is about solving problems!

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curiousDog
He has great notes. I have to thank him sometime for helping me test out of
Linear Algebra and help skip a class.

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code5fun
This is amazing! Thanks for the effort!

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arvinsim
I wish I had these resources a decade ago when I was still in college. It
would have helped immensely.

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nadinno78
Me too. Was browsing this one site recently
[http://betterexplained.com/](http://betterexplained.com/)

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Nickersf
This site mixed with Patrick jmt's videos tends to help me more than lectures.

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Undertow_
I've got an AP test coming up. This should come in handy.

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DarkContinent
These saved my Honors Calc III grade this semester :)

