Mysterious Holes || Mathematical Analysis || Repeated Series

[@declanfarber]

Apostol and Feynman were contemporaries, and both taught introductory courses at Caltech around that time (ca 1960 give or take.) This is an interesting insight into what it was like to be at that school at that time. The picturing of it is interesting. To be a fly on the wall. Yeah go ahead and smell the binding. :^)

[@TheMathSorcerer]

Oh wow how interesting!!

[@premkumar-so3ff]

Although Apostol book is classic and regularly used as reference with rudin , both doesn't give explanation when something needs to do. Possibly since they written sometime before 1970s that's the way they go around that time. I would prefer book like Robert Strichartz The Way Of Analysis as initial beginner friendly yet has theorems that been in rudin or apostol. Reviewing that book is good since I feel like studying along that book covers much of short book of rudin or lengthy one of apostol.

[@navierstokes2356]

I think it would be easier to visualize what it's actually happening if you would put a matrix, then one order of the series is column sum and the other order is row sum.

[@Maths_3.1415]

You are the unsolved problem of mathematics :)

[@alexfekken7599]

I think that's an understatement: visualising it in that way makes it completely trivial as well as easy to remember: |0|-|0|0|0... |+|0|-|0|0|.. |0|+|0|-|0|... |0|0|+|0|-|... ... etc, (using a non-proportional font or a better artist)

[@ColonelPanic007]

I greedily guard my Apostol books. His work with The Mechanical Universe television series and the MU text got me interested in Mathematics.

[@TheMathSorcerer]

nice:)

[@OleJoe]

I met Tom Apostol once back in the early 1980s at CSULB when I was in grad school. One of my math professors knew Apostol and invited him to give a lecture on Analytic Number Theory. Something I knew nothing about and still don't. I went to the lecture just to be there. Got to meet and talk to him afterwards.

[@TheMathSorcerer]

Wow !!

[@johnflorio3576]

We used the Apostol text for Mathematical Analysis in graduate school. It was intimidating at first but thankfully we had a professor who was an outstanding communicator.

[@TheMathSorcerer]

that's awesome:)

[@Anonymous-qw]

I used this Apostol book for my second year Analysis Couse for for my Bsc(Hons) Mathematics degree in the UK in the early 1980s. It is one of the books I still have and survived my ex wife who wanted to take all my old college books to a second hand book shop. My copy is a blue paperback. As paperbacks get damaged much more easily it is in a much less good condition than yours. I found it quite terse as well. I also used Dellillo Advanced Calculus with Applications for that course.

[@mentatphilosopher]

So I thought I would follow along with my second edition from September 73. There has been a good amount of changes. It looks like a lot of the elementary vector calculus went elsewhere; the total page count is smaller at 492. The “repeated series” is now called “integrated series” and the “important case” must no longer be important as it has disappeared completely.

[@edwardgraham2566]

I always love your review of mathematical book reviews --- thank you!

[@tmendoza6]

staples someone gone mad by analysis thinking he can gain a firm understanding love it great video!

[@hussainfawzer]

Though I’ve never seen double summation ever before. I understood your explanation. I feel very happy. 😊

[@TheMathSorcerer]

😊😊😊😊

[@sanjitdas5418]

I remember when I bought the first copy (Calculus, vol1) -- in 1999-- red Wiley soft cover-- It was written dedicated to Jane and Stephen! Much later (two years later) I came to know about this book.

[@physicshypernova2083]

I have this one as well. It was helpful in understanding winding numbers when I was preparing for my qualifying presentation for my PhD. The calculus book by Courant was also useful and easier to read than Apostol.

[@Zone_Stomper]

You should try your hand at book repair as you have some in need of fixing. If successful, you can show the before and after along with the affiliate link for a book binding and repair kit.

[@TheMathSorcerer]

I have some REALLY old books from the 1800's that are just falling to pieces. I should look into how to fix those. They are readable but they are falling apart.

[@Zone_Stomper]

@@TheMathSorcerer Other content creators have made viral videos on repairing old things. I will stay tuned but know that it's the kind of thing that could take some time. Looking forward to it.

[@xAssailantx]

"this math book has been damaged..." Literally the most perfect condition Tom Apostol textbook I've ever seen. Probably worth like 500 dollars.

[@gmcenroe]

At 12:17 you have the series where m=3 but it looks like you wrote f(3,2) = -1 and f(3,4) =1. Shouldn't fI3,2)=1 and f(3,4)= -1 so you ended up with the correct sum of 0 but individual values were reversed. You said f(3,2) is 1 and f(3,4) is -1 but then wrote the incorrect values. Please correct me if I am wrong. Sorry for being picky. Thanks looks like a good book.

[@nice5557]

I saw it explains Cesaro Summability (3:18) which is quite unexpected for the introductory level.

[@dd-uf9nw]

I'm currently working on apostol cal.1 but i liked it so much that I would also go for his cal2 and mathematical analysis.

[@spacetimemalleable7718]

Please review Apostol's two volume Calculus books. They are my favorite Calculus books.

[@paulkarch3318]

When I took calculus, our professor used his book. I found it a little bit hard because I went to a rural high school and I had never seen anything like that before. He begins the book with integral calculus and uses the method of exhaustion known to the Greeks to essentially compute the Riemann integral of a function.

[@temperedwell6295]

Ahh, the good old days, when an author could assume that anyone interested in reading his book could figure out a lot of things on his own.

[@John_Smith__]

Yup Tom Apostol Calculus is very very popular. He does have a two volumes book that covers a lot of Calculus. Well written book no doubt.

[@licorice4956]

Do you have Mathematical Analysis by Zorich? It's also a famous analysis book, though primarily used in eastern countries.

[@viniciusbocchi3739]

Best analysis book ever written!

[@brianstevens3858]

Staples, we haven't always used stretch wrap to bind pelleting, and accidents happen.

[@niket527]

Can you review the regular calculus apostol book?

[@tamaramacadam8650]

Oooh yesterday I found this book at my uni library! World Student Series edition, second printing (1965). Definitely going to work through it over the next couple months.

[@moontiger6393]

Draw a grid with values of m as columns and values of n as rows, and fill in the squares with -1, 1 and 0 appropriately, the reason the two sums are not equal then becomes apparent. I should note that almost the exact same idea appears in an exercise in Donald Knuth's Concrete Mathematics (Exercise 2.28 to be exact)

[@griffgruff1]

This brought back memories. I bought my copy of this book in 1970.

[@jennifertate4397]

Bedbugs with fierce stingers who like mathematics.

[@BrainDonors]

We need bulk books review like you are doing in math sorcerer espanol

[@homamthewise6941]

Great vid as always

[@SequinBrain]

0:18 3 staples caused that

[@larry_the]

If this is a book that contained a dust jacket it is possible someone tried to ensure it stays on by using staples or something similar.

[@jameyatesmauriat6116]

Nice explanation and problem working! Can I know when your udemy courses would be on discount? Last time I only subscribed to one calculus course and was in discount.. Thank you

[@davidrandell2224]

One wonders why Galilean relative motion is such a difficult subject. D=1/2at^2 describes the ‘motion ‘ of the released object or the ‘motion ‘ of the earth towards the released- and now stationary- object. Only 50% “ chance “ one or the other is correct. Any accelerometer- slinky, water balloon or phone app- proves the earth is expanding at 16 feet per second per second constant acceleration. Yet such exceeds the modern brain’s ability. Gravity right there in all it’s glory.

[@davidnelson4960]

Great stuff

[@hiroshibuya8284]

Please, can you do a video reading a book from 19th century about conics on a deserted beach?? 🙏🏻🙏🏻🙏🏻

[@TheMathSorcerer]

I could actually do that lol and it sounds like fun!!!!

[@BShelled]

do those holes not look like they were made by a staple?

[@craigdupree1687]

The holes in the book are from someone repeatedly stabbing it with a pencil which anyone that that has ever gotten stuck on a proof will understand.

[@TheMathSorcerer]

LOL!!

[@JimFarrand]

Has it been stabbed with a compass? (As in compass and straight edge.) Seems like the only piecing weapon one might have to hand in a maths classroom.

[@Maths_3.1415]

Thank you for such a good book :)

[@sandeeprawan9280]

Hello good morning sir how r u sir how can I got this book sir reply me please sir

[@TheMathSorcerer]

I put a link in the description to a few different versions.

[@cedricvillani8502]

But Zero doesn’t actually exist in the real world right?

[@ianmorgan7906]

That whiff.....

[@fernandocupil.6463]

Yo quiero comprar este libro. Pero no lo encuentro en pasta dura :( Ojalá en el futuro puedan sacar más versiones en hardcover.

[@crcaccounts]

Great title...

[@michaelhartl]

Cool, I knew about Tom Apostol’s calculus texts (for years known at Caltech as “Tommy 1” and “Tommy 2”) but didn’t know he also wrote a more advanced text on mathematical analysis. Incidentally, the “t” in “Apostol” is silent, so it’s pronounced like the English word “apostle” (which of course also has a silent “t”). You can hear the pronunciation near the start of this video from 2013: kzbin.info/www/bejne/bJrQh41tpMyjd6c

[@stevenkies802]

Those holes look like someone stapled paper to the cover.

[@ppp3812]

Would you mind enabling captions?

[@TheMathSorcerer]

Yeah they should get automatically published after a while I think.

[@oooltra]

How fancy is it on a scale of 1 to 11?

[@ronbackal]

Apostol was communicating with aliens! They used to holes to communicate :-)

[@ardiris2715]

"This week's assignment is finding the typo in question 14. Show all work." (:

[@vrclckd-zz3pv]

Me: \*Walks into a truck stop bathroom* The cubicle walls:

[@ManuelGarcia-ww7gj]

Ice-a-pick!

[@RoscoesRiffs]

🐛 Book worms. 🐛

[@Zone_Stomper]

first

[@mariadelourdesaniessanchez1473]

Iam doing in the school Jesus

[@mariadelourdesaniessanchez1473]

I study in the school

[@Antiwasserstoff]

Those holes look like bite marks from a cat. Don't believe me? I've got some books which my cat actually bit and scratched and it just looks like this

[@JS-jh4cy]

Book worms? Or book bed bug?

[@Matlockization]

Staple marks. Mathematical problem solved.

[@henriquel8757]

Maybe someone who was trying to understand the subject got angry and decided to poke the book using a compass.😅

[@TheMathSorcerer]

LOL

[@frogmcribbit8778]

Reject modern math, return to rule and compass.

[@orsisrutherford4705]

Staple holes

[@JohnVKaravitis]

Smallpox. It's been nice knowing you!