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Math notes to take you from one year of college calculus to grad student level

math.ucr.edu

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Re: Math notes to take you from one year of college calculus to grad student level

#41

Post by doktrin »

ams6110 wrote: post #36
doktrin wrote: post #30

Earlier quoted context omitted.

>> if you really wanted to learn this material, then you would have started already This is pretty much the only statement i have an objection or reaction to. I simply don't understand the basis for assertions along these lines. These sorts of fatalistic proclamations are made not-infrequently in the context of programming and development as well. Its as if we feel that the only ones worthy of pursuing a given discip…

This kind of mathematics is at a level that requires a certain amount of self-motivation, passion, desire, whatever you want to call it, to learn. It's probably something you're born with, which is why not many people pursue graduate studies in mathematics and those who do are mostly people with a real love for it. It's unlikely that at some point in your adult life you're going to suddenly develop the necessary burn…

>> It's probably something you're born with

What are you basing this claim on?

>> It's unlikely that at some point in your adult life you're going to suddenly develop the necessary burning desire to motivate such study

While it's true that adults are not likely to re-enroll in University to study mathematics, that doesn't necessarily mean the desire isn't there.

For instance, a "burning" desire may be sufficient to motivate a 22 year old to study mathematics, however that same desire in a 44 year old might not overcome the pressures, realities and obligations of life, work & family.

Re: Math notes to take you from one year of college calculus to grad student level

#42

Post by doktrin »

SandB0x wrote: post #34
doktrin wrote: post #30

Earlier quoted context omitted.

>> if you really wanted to learn this material, then you would have started already This is pretty much the only statement i have an objection or reaction to. I simply don't understand the basis for assertions along these lines. These sorts of fatalistic proclamations are made not-infrequently in the context of programming and development as well. Its as if we feel that the only ones worthy of pursuing a given discip…

I agree with your sentiment. Sometimes we get articles on (say) the Fourier transform, with its own intuitive take on how and why it works, some visualisation and some maths. I think these articles are great. I can understand how they would spark the interest of someone who is not familiar with the maths, whatever their age. That's not the case here. I don't think that anyone who has upvoted this has read any signifi…

Fair. I happen to agree that the document is probably not going to be of much use to anyone who hasn't already studied the material.

I do, however, firmly believe that anyone - no matter their age - may find interest and cause to learn math, even if starting with high school calculus.

Re: Math notes to take you from one year of college calculus to grad student level

#44

Post by olympus »

dmcdougall_ wrote: post #6
xxpor wrote: post #4

I found the writing style to be incredibly obnoxious and hand wavy, and really make me stop reading.

Admittedly, I stopped before then when I saw the poor mathematics rendering. For some reason unbeknownst to me, the equations appear cramped and difficult to read.

I'm pretty sure I know the guy that wrote this (seriously, how many physicists named Alex Alaniz are there?), and he can't have LaTeX on his work computer because of some really dumb rules. So I don't blame him for it being an exported Word document because a LaTeX version would have meant doing this all at home instead of his spare time at work.

Re: Math notes to take you from one year of college calculus to grad student level

#45

Post by alexkus »

doktrin wrote: post #41
ams6110 wrote: post #36

Earlier quoted context omitted.

This kind of mathematics is at a level that requires a certain amount of self-motivation, passion, desire, whatever you want to call it, to learn. It's probably something you're born with, which is why not many people pursue graduate studies in mathematics and those who do are mostly people with a real love for it. It's unlikely that at some point in your adult life you're going to suddenly develop the necessary burn…

>> It's probably something you're born with What are you basing this claim on? >> It's unlikely that at some point in your adult life you're going to suddenly develop the necessary burning desire to motivate such study While it's true that adults are not likely to re-enroll in University to study mathematics, that doesn't necessarily mean the desire isn't there. For instance, a "burning" desire may be sufficient to m…

> For instance, a "burning" desire may be sufficient to motivate a 22 year old to study mathematics, however that same desire in a 44 year old might not overcome the pressures, realities and obligations of life, work & family.

You'd be surprised at how many there are.

I'm mid-30s and I've recently finished a maths degree via distance learning (Open University in the UK). During the time I've been studying I've moved house, got married, had increased work pressures, become a father and I am helping bootstrap a startup in what little free time is left from all of that.

At the various tutorials, revision day schools and exams during my studies I met lots of others who were in similar positions. It's more common than you think.

Re: Math notes to take you from one year of college calculus to grad student level

#46

Post by crntaylor »

ajtulloch wrote: post #35

If you're interested in this material, you may also like my LaTeX'ed lecture notes covering the last few years of my mathematics degree - mostly pure mathematics with some statistics and financial mathematics. http://tullo.ch/2011/mathematics-lecture-notes/ for the PDFs, and https://github.com/ajtulloch/SydneyUniversityMathematicsNote... for the LaTeX source.

This looks really neat. Nice work!

Re: Math notes to take you from one year of college calculus to grad student level

#47

Post by crntaylor »

jfarmer wrote: post #38

I can't stand the sans serif typesetting and cramped mathematical formulas. The tone is kind of obnoxious, too. When he introduces group theory: Group theory basics. It is time to note that our one-parameter symmetries are groups in the sense of modern algebra. Why? To masturbate with nomenclature as you do in an abstract algebra class? No. Because, as you will soon see, studying the group structure of a symmetry of…

What really struck me about that lecture is that he only uses one blackboard throughout the entire talk, and he doesn't start writing on it until 20 minutes in. I wish more lectures and talks were like that.

Re: Math notes to take you from one year of college calculus to grad student level

#48

Post by atondwal »

sambomillo wrote: post #17

I'm sorry, grad student level on just notes? I don't think so. Maybe grad degress aren't worth what they used to be, but certainly more than notes.

Well, there's a difference between holding-a-grad-degree level, and being a grad student. On the other hand if the implication was that undergrad degrees teach your relatively little in comparison to what they should, then yes.

Re: Math notes to take you from one year of college calculus to grad student level

#49

Post by Confusion »

SandB0x wrote: post #28

I'm surprised by the excitement at every piece of teaching material or set of course notes posted here. Free textbooks and PDF notes have been around for years, especially for mathematical topics. This PDF won't do the work for you, and you can't skim-read this kind of material. To properly understand an area of mathematics then you need to put a significant amount of time and effort into working through the text, an…

  if you really wanted to learn this material you would have 
  started already.
People change.

Re: Math notes to take you from one year of college calculus to grad student level

#50

Post by Vivtek »

alexkus wrote: post #45
doktrin wrote: post #41

Earlier quoted context omitted.

>> It's probably something you're born with What are you basing this claim on? >> It's unlikely that at some point in your adult life you're going to suddenly develop the necessary burning desire to motivate such study While it's true that adults are not likely to re-enroll in University to study mathematics, that doesn't necessarily mean the desire isn't there. For instance, a "burning" desire may be sufficient to m…

> For instance, a "burning" desire may be sufficient to motivate a 22 year old to study mathematics, however that same desire in a 44 year old might not overcome the pressures, realities and obligations of life, work & family. You'd be surprised at how many there are. I'm mid-30s and I've recently finished a maths degree via distance learning (Open University in the UK). During the time I've been studying I've moved…

So you're actually proving the point: you weren't born with this burning desire, you didn't learn it in college or high school or (as burning desire would indicate) when you were twelve - you waited until now, and were perfectly capable of learning it once your motivations changed.

As they do, as time passes. Anybody out of their 20s will know that.

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