4 ms·

I find that reading math at all is sometimes not the best approach. When working out of a textbook I often find it more constructive to attempt problems first a

by SOTGO 4y ago

I find that reading math at all is sometimes not the best approach. When working out of a textbook I often find it more constructive to attempt problems first and then use the text as a guide to help me solve the problem, particularly when the textbook is quite dense. For example, even after taking years of analysis I still find Rudin impossible to simply "read" because the mathematics is so condensed and difficult to follow.

codethief 4y ago
When you say "Rudin" which one do you mean? Big Rudin? Baby Rudin?
vector_spaces 4y ago
I know he gets a lot of hate, but I personally love Rudin's writing style. There are more chatty analysis textbooks like Abbott and Carothers, but the conciseness of Rudin plays nicest with the way I think, and the exercises (in Baby Rudin) are really wonderful. They're hard but I usually felt a genuine sense of accomplishment when I finished one Chattier authors are nice for providing context and intuition and sometimes details about the historical context, but I personally find them to be very distracting and a bit overwhelming. I don't like using them for much other than a reference or more casual reading. On the other hand, I loved reading a few sentences from Rudin that I didn't quite follow, then pulling out some pen & paper and doing a quick validation, or even going on a drive and munching on them until I understood That's me though. I'm glad that there seems to be no shortage of introductory analysis texts written in all kinds of styles so that folks can find the ones that work best for them. As an aside, I think it's a bummer that analysis classes often feel like hazing courses in the math curriculum, leading many mathematicians to despise it. I've been very lucky to have great analysis teachers, or at least ones that care very much about pedagogy over ruthless elitism, and conveying the beauty and fun that lies amid the ugly bit :) Also, re Rudin: his autobiography is certainly worth reading, if for no other reason than for his account of surviving the Anschluss (the Nazi annexation of Austria during WWII) as a young Jew. One of my favorite bits: "On the first day of school after the Anschluss several of our teachers and even some students strutted around in their shit-colored storm trooper uniforms. (The Nazi party had been illegal, but had obviously existed.) One of those was the gym teacher whom I had always disliked. He even had a pistol strapped to his belt. A few days later I heard that he had shot himself in the foot. This was one of the very few bits of cheerful news at the time." It's a fairly harrowing read, and perhaps some of his best writing overall
- keithalewis 4y ago
  I asked Walter about this when I was a grad student at University of Hawaii. He and his wife Mary Ellen would visit regularly and I was attempting to make small talk at a pau hana party. He said he made an effort to find the shortest proofs of all the basic theorems so students could get to the more interesting results quicker.
- peterhalburt33 4y ago
  The first time I attempted Rudin I gave up after the second chapter. I had been through Abbot, and still didn’t truly understand Analysis (or the style of analysts). After letting it sit for a few months, I picked Rudin back up and it instantly became my favorite text. I have no clue why this change happened so suddenly, but as a convert I will point out that he is a master at including exactly the right amount of detail: he does not leave details out, but neither does he commit the equally (if not more) harmful sin of over explaining a concept. This leaves every concept explained as concisely and simply as possible, but no more, and is extremely helpful as a person with ADHD. The book is worth it’s weight in gold: one can read a chapter of Rudin in a day and have a better understanding of the concept than reading twice or three times as much material in a competing analysis text.

by SOTGO 4y ago

codethief 4y ago

When you say "Rudin" which one do you mean? Big Rudin? Baby Rudin?

vector_spaces 4y ago

I know he gets a lot of hate, but I personally love Rudin's writing style. There are more chatty analysis textbooks like Abbott and Carothers, but the conciseness of Rudin plays nicest with the way I think, and the exercises (in Baby Rudin) are really wonderful. They're hard but I usually felt a genuine sense of accomplishment when I finished one Chattier authors are nice for providing context and intuition and sometimes details about the historical context, but I personally find them to be very distracting and a bit overwhelming. I don't like using them for much other than a reference or more casual reading. On the other hand, I loved reading a few sentences from Rudin that I didn't quite follow, then pulling out some pen & paper and doing a quick validation, or even going on a drive and munching on them until I understood That's me though. I'm glad that there seems to be no shortage of introductory analysis texts written in all kinds of styles so that folks can find the ones that work best for them. As an aside, I think it's a bummer that analysis classes often feel like hazing courses in the math curriculum, leading many mathematicians to despise it. I've been very lucky to have great analysis teachers, or at least ones that care very much about pedagogy over ruthless elitism, and conveying the beauty and fun that lies amid the ugly bit :) Also, re Rudin: his autobiography is certainly worth reading, if for no other reason than for his account of surviving the Anschluss (the Nazi annexation of Austria during WWII) as a young Jew. One of my favorite bits: "On the first day of school after the Anschluss several of our teachers and even some students strutted around in their shit-colored storm trooper uniforms. (The Nazi party had been illegal, but had obviously existed.) One of those was the gym teacher whom I had always disliked. He even had a pistol strapped to his belt. A few days later I heard that he had shot himself in the foot. This was one of the very few bits of cheerful news at the time." It's a fairly harrowing read, and perhaps some of his best writing overall

keithalewis 4y ago
I asked Walter about this when I was a grad student at University of Hawaii. He and his wife Mary Ellen would visit regularly and I was attempting to make small talk at a pau hana party. He said he made an effort to find the shortest proofs of all the basic theorems so students could get to the more interesting results quicker.
peterhalburt33 4y ago
The first time I attempted Rudin I gave up after the second chapter. I had been through Abbot, and still didn’t truly understand Analysis (or the style of analysts). After letting it sit for a few months, I picked Rudin back up and it instantly became my favorite text. I have no clue why this change happened so suddenly, but as a convert I will point out that he is a master at including exactly the right amount of detail: he does not leave details out, but neither does he commit the equally (if not more) harmful sin of over explaining a concept. This leaves every concept explained as concisely and simply as possible, but no more, and is extremely helpful as a person with ADHD. The book is worth it’s weight in gold: one can read a chapter of Rudin in a day and have a better understanding of the concept than reading twice or three times as much material in a competing analysis text.