Should I Become a Mathematician?

[RJinkies]

mathwonk - for old books, (around 1900), i like goursat's course in analysis, 3 volumes, recommended by that cranky brilliant russian mathematician, arnol'd.

Not that easy to find at one time, since libraries usually got tons of the french copies and there were 1910's translations too by Ginn and sold em for a few decades, and dover finally did a Phoenix hardcover of them. Hardy was really a huge fan of Goursat and that was a influence for him.

I remember seeing stuff nicely stated, but i wondered just how good one's french would need to be to tackle that and what level someone to be tackling it, with no analysis, with some analysis etc etc... but i do remember out of the blue little hunks of set theory would be tossed in with wonderfully crisp and strange fonts and then there was talk about a Jordan curve, and only later with Parke i said, oh it's in english, funny how the uni library didnt have a copy of that.

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did you like any of the 60s and 70s calculus texts out there, aside from the one's you mentioned and used? I remember seeing a lot of odd experimental 60s texts, maybe 70% of them seemed stiff with a lot of bland robotic New math formalism, which felt like all the set theory and analysis parts of Dolciani hatched on you. the 1960s New American Landau...

there were a lot of other texts out there than thomas/finney and Stewart... thinks like Campbell and Dierker or Harley Flanders gets lost in the cracks of out print books

I thought Campbell/Dierker [late 70s] was dull and i think Marsden and others did a good book in the 70s and 80s for calculus, maybe not the most gentle though. Flanders i liked but i was bothered a great deal with his suggestions for students to do all these sloppy freehand like scribbles and stuff

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Parke does mention goursat for advanced calculus
[things like Goursat/Hardy/Franklin's other book/Rudin are really analysis courses but closely bundled here]

Calculus: Advanced - Chronological - Title
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Wilson 12 - Advanced Calculus [Ginn] - 566 pages
Bliss 13 - Fundamental Existence Theorems [American Mathematical Society] - 107 pages
Hardy 16 - 2e - The Integration of Functions of a Single Variable [Cambridge] - 67 pages
Goursat 04-17 - A Course in Mathematical Analysis [Ginn]
Edwards 22 - The Integral Calculus [2 volumes] [Chelsea] - 1922 pages
Osgood 25 - Advanced Calculus [Macmillian] - 530 pages
Fine 27 - Calculus [Macmillian] - 421 pages
Landau 30 - Foundations of Analysis [Chelsea] [published in German 1930 translated 1951] - 134 pages
Woods 34 - Advanced Calculus: a Course Arranged with Special Reference to the Needs of Students of Applied Mathematics [Ginn] - 397 pages
Chaundy 35 - The Differential Calculus [Oxford] - 459 pages
Courant 38 - Differential and Integral Calculus [2 volumes] [Interscience/Blackie/Nordemann]
Burrington 39 - Higher Mathematics with Applications to Science and Engineering [McGraw-Hill] - 844 pages
Gillespie 39 - Integration [Oliver and Boyd] - 126 pages
Franklin 40 - A Treatise on Advanced Calculus [Wiley] - 595 pages
Stewart 40 - Advanced Calculus [Methuen]
Sokolnikoff 41 - 2ed - Advanced Calculus [McGraw-Hill] - 587 pages
Franklin 44 - Methods of Advanced Calculus [McGraw-Hill] - 486 pages
Hardy 45 - 8e - A Course of Pure Mathematics [Cambridge] - 500 pages
Widder 47 - Advanced Calculus [Prentice-Hall] - 432 pages
Gillespie 51- Partial Differentiation [Oliver and Boyd/Interscience] - 105 pages
Kaplan 51 - 2e - Advanced Calculus for Engineers and Physicists [Ann Arbor] - 338 pages
Wylie 51 - Advanced Engineering Mathematics [McGraw-Hill] - 640 pages
Hardy 52 - 10e - A Course of Pure Mathematics [Cambridge] - 509 pages
Kaplan 52 - Advanced Calculus [Addison-Wesley] - 679 pages
Rudin 52 - Principles of Mathematical Analysis [McGraw-Hill] - 227 pages

[I got Woods, Courant, Franklin [his analysis book, the calculus one is in the basic calculus list], Sokolnikoff [i thought it was way easier than Thomas and Finney and gentle], Hardy, and i think i got either Widder or Kaplan, but not both, maybe]

[I seen Edwards, and Landau and Rudin but didnt find any copies when i was collecting them]


what else would you [or anyone else] name drop from the 50s 60s 70s, that you haven't mentioned before that you think might be almost as neat as Courant, Kaplan or Widder?

I used to think that pre 1970 most any McGraw-Hill text was mainstream in the schools, and well anything from the 40s to now Addison-Wesley never did a bad textbook.

I always wondered why Ginn, Macmillian and also Blakiston would seem to be receding from the 50s to now from the textbook market, usually Ginn and Macmillian always wanted to cater to the old style high school textbooks, and i think as competition grew esp after sputnik, they both shrank, but people still use a number of their classic texts for reading...

lets add the MAA elementary calc books:

MAA: Elementary Calculus

1968
Levi, Howard. Polynomials, Power Series, and Calculus New York, NY: Van Nostrand Reinhold, 1968.
*** Thomas, George B., Jr. and Finney, Ross L. Calculus and Analytic Geometry, Reading, MA: Addison-Wesley, 1968, 1987. Seventh Edition.

1972
Dorn, William S.; Bitter, Gary G.; and Hector, David L. Computer Applications for Calculus Boston, MA: Prindle, Weber and Schmidt, 1972.

1975
Swokowski, Earl W. Calculus, Boston, MA: PWS-Kent, 1975, 1991. Fifth Edition.

1976
* Keisler, H. Jerome. Foundations of Infinitesimal Calculus Boston, MA: Prindle, Weber and Schmidt, 1976.
* Keisler, H. Jerome. Elementary Calculus, Boston, MA: Prindle, Weber and Schmidt, 1976, 1986. Second Edition.
* Lax, Peter; Burstein, Samuel; and Lax, Anneli. Calculus with Applications and Computing New York, NY: Springer-Verlag, 1976.

1977
* Goldstein, Larry J.; Lay, David C.; and Schneider, David I. Calculus and Its Applications, Englewood Cliffs, NJ: Prentice Hall, 1977, 1990. Fifth Edition.
* Kline, Morris. Calculus: An Intuitive and Physical Approach, New York, NY: John Wiley, 1977. Second Edition.

1979
Henle, James M. and Kleinberg, Eugene M. Infinitesimal Calculus Cambridge, MA: MIT Press, 1979.
** Priestley, William M. Calculus: An Historical Approach New York, NY: Springer-Verlag, 1979.

1980
* Anton, Howard. Calculus with Analytic Geometry, New York, NY: John Wiley, 1980, 1988. Third Edition.
Bittinger, Marvin L. Calculus: A Modeling Approach, Reading, MA: Addison-Wesley, 1980, 1988. Fourth Edition.
** Spivak, Michael D. Calculus, Boston, MA: Publish or Perish, 1980. Second Edition.

1982
** Stein, Sherman K. Calculus and Analytic Geometry, New York, NY: McGraw-Hill, 1982, 1987. Fourth Edition.

1985
Ash, Carol and Ash, Robert B. The Calculus Tutoring Book Los Angeles, CA: IEEE Computer Society, 1985.
* Hamming, Richard W. Methods of Mathematics Applied to Calculus, Probability, and Statistics Englewood Cliffs, NJ: Prentice Hall, 1985.
* Marsden, Jerrold E. and Weinstein, Alan. Calculus, New York, NY: Springer-Verlag, 1985. Second Edition.
* Simmons, George F. Calculus with Analytic Geometry New York, NY: McGraw-Hill, 1985.

1988
Grossman, Stanley I. Calculus, San Diego, CA: Harcourt Brace Jovanovich, 1988. Fourth Edition.

1989
Berry, John; Norcliffe, Allan; and Humble, Stephen. Introductory Mathematics Through Science Applications New York, NY: Cambridge University Press, 1989.

1990
* Finney, Ross L. and Thomas, George B., Jr. Calculus Reading, MA: Addison-Wesley, 1990.
Fraleigh, John B. Calculus with Analytic Geometry, Reading, MA: Addison-Wesley, 1990. Third Edition.
Seeley, Robert T. Calculus San Diego, CA: Harcourt Brace Jovanovich, 1990.
Small, Donald B. and Hosack, John M. Explorations in Calculus with a Computer Algebra System New York, NY: McGraw-Hill, 1990.
Small, Donald B. and Hosack, John M. Calculus: An Integrated Approach New York, NY: McGraw-Hill, 1990.

1991
Feroe, John and Steinhorn, Charles. Single Variable Calculus with Discrete Mathematics San Diego, CA: Harcourt Brace Jovanovich, 1991.
** Strang, Gilbert. Calculus Wellesley, MA: Wellesley-Cambridge Press, 1991.

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and the higher up MAA calculus books:

MAA: Advanced Calculus

1937
*** Courant, Richard. Differential and Integral Calculus, New York, NY: Interscience, 1937. 2 Vols.

1952
* Kaplan, Wilfred. Advanced Calculus, Reading, MA: Addison-Wesley, 1952, 1984. Third Edition.

1956
* Knopp, Konrad. Infinite Sequences and Series Mineola, NY: Dover, 1956.

1959
*** Hardy, G.H. A Course of Pure Mathematics New York, NY: Cambridge University Press, 1959.

1962
Hildebrand, Francis B. Advanced Calculus for Applications, Englewood Cliffs, NJ: Prentice Hall, 1962, 1976. Second Edition.

1965
Bromwich, Thomas J. l'Anson. An Introduction to the Theory of Infinite Series New York, NY: Macmillan, 1965.
** Buck, R. Creighton. Advanced Calculus, New York, NY: McGraw-Hill, 1965, 1978. Third Edition.
Landau, Edmund G.H. Differential and Integral Calculus New York, NY: Chelsea, 1965.
*** Spivak, Michael D. Calculus on Manifolds Reading, MA: W.A. Benjamin, 1965.

1967
*** Apostol, Tom M. Calculus, New York, NY: John Wiley, 1967, 1969. 2 Vols., Second Edition.

1969
Cronin-Scanlon, Jane. Advanced Calculus: A Start in Analysis, Lexington, MA: D.C. Heath, 1969. Revised Edition.
Fulks, Watson. Advanced Calculus, New York, NY: John Wiley, 1969, 1978. Third Edition.

1972
Williamson, Richard E.; Crowell, Richard H.; and Trotter, Hale F. Calculus of Vector Functions, Englewood Cliffs, NJ: Prentice Hall, 1972. Third Edition.

1973
** Schey, H.M. Div, Grad, Curl, and All That: An Informal Text on Vector Calculus New York, NY: W.W. Norton, 1973.

1974
Sagan, Hans. Advanced Calculus of Real-Valued Functions of a Real Variable and Vector-Valued Functions of a Vector Variable Boston, MA: Houghton Mifflin, 1974.

1976
** Marsden, Jerrold E. and Tromba, Anthony J. Vector Calculus, New York, NY: W.H. Freeman, 1976, 1988. Third Edition.

1980
Amazigo, John C. and Rubenfeld, Lester A. Advanced Calculus and Its Applications to the Engineering and Physical Sciences New York, NY: John Wiley, 1980.

1982
* Simmonds, James G. A Brief on Tensor Analysis New York, NY: Springer-Verlag, 1982.

1983
Taylor, Angus E. and Mann, W. Robert. Advanced Calculus, New York, NY: John Wiley, 1983. Third Edition.

1984
Price, G. Baley. Multivariable Analysis New York, NY: Springer-Verlag, 1984.

1985
* Marsden, Jerrold E. and Weinstein, Alan. Calculus III, New York, NY: Springer-Verlag, 1985. Second Edition.

1986
Grossman, Stanley I. Multivariable Calculus, Linear Algebra, and Differential Equations, New York, NY: Academic Press, 1986. Second Edition.

1987
* Widder, David V. Advanced Calculus, Mineola, NY: Dover, 1987. Second Edition.

1988
Bamberg, Paul and Sternberg, Shlomo. A Course in Mathematics For Students of Physics, New York, NY: Cambridge University Press, 1988, 1990. 2~Vols.
Magnus, Jan R. and Neudecker, Heinz. Matrix Differential Calculus with Applications in Statistics and Econometrics New York, NY: John Wiley, 1988.

1989
** Courant, Richard and John, Fritz. Introduction to Calculus and Analysis, New York, NY: Springer-Verlag, 1989. 2 Vols. [this should be like 1965-1966]

1990
* Knopp, Konrad. Theory and Application of Infinite Series Mineola, NY: Dover, 1990.
Loomis, Lynn H. and Sternberg, Shlomo. Advanced Calculus, Boston, MA: Jones and Bartlett, 1990. Revised Edition.

1991
* Bressoud, David M. Second Year Calculus New York, NY: Springer-Verlag, 1991.

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there has to be some mid-late 50s , 60s 70s 80s books slipped through the cracks with the MAA list...

again, i always wondered why they cut out the older titles, their recommendations would keep things in print, and i guess there is always a bias for something 'new' to keep 'some' people busy lol

[and i would definitely think that the dates and judging of the different editions would have been liked too]

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[mathwonk]

all the books in those days were good. even the routine books were good, like kiokemeister; thomas; smith, granville and stewart?,

then there were good books that never caught on like the one by lipman bers, and quirky but interesting ones like harley flanders, or m.e.munroe.

strong classic style books included buck, widder, and so on.

the three excellent new 1960's books were by apostol, spivak, and joseph kitchen.

flaky, over the top books included spencer steenrod and nickerson, which i have never heard of anyone learning from.

another one is loomis and sternberg.

really good new advanced calc books include wendell fleming, spivak, apostol.

but really one only needs one good book to read.my goursat is translated into english, by hedrick i think, indeed pub. by Ginn, 1904(vol 1), 1916 (vol2), 1917(vol3).

 

[RJinkies]

- all the books in those days were good. even the routine books were good, like kiokemeister; thomas; smith, granville and stewart?

So true... i just remember thinking that all the 60s textbooks for physics and math seemed to offer just all that 'extra' detail. And one felt that a lot of books or texts where they cram something into 'one semester' should be two semesters with books like that. [Which was true of Symon for mechanics]

A slower pace, as well as starting with basics and handholding for the first 100 pages, but by the time you're at the end of the book, you feel like you were pushed into something like the top elite of Feynman's lectures or Hardy..

I think it was easier say before 1968, or possibly in other things before Sputnik where you almost got algebra and calculus in your first year uni, because the schools didnt trust the high schools to teach alike... As well as showing you 'how to study'...The older books are harder, occasionally clunky, and sometimes a more leisurely pace, or 30% to 300% times the content of most 70s 80s 90s texts that are all watered down.

but if you can get through them, or part way through... [one chapter is a lifetime of accomplishment - is one of my mantras] i think you come out with a pretty neat outlook and a unique box of tools...

and that goes for a schaums outline as well. There's something there about just seeing example upon example, almost like 20 fold what a teacher could explain on a blackboard and if you're lazy, or you're really out to bash yourself out knowing some of them inside out... you can definitely get something different out of the experience.

I think schaums outlines threw out a need for 'more problems' and 'worked out problems' which is basically what a teacher does at the damn blackboard. Which in fact makes something like a schaum's outline way way more something to treasure than taking a class and seeing the lectures.

ideally you got a great text, great supplementary texts, infinite hours to burn reading, and doing problems, enough patience to see that xx hours a week will get results out of a textbook, a great teacher and hopefully something like a schaum's outline.

But i think a lot of physics books and math books in the late 60s started to wake up and by the 70s you saw books adding more problems and then more problems, and still more worked out problems, to address what they lacked, and what schaum's offered.

I heard a rumour that schaum's outlines were like collections of problems from all the major texts of the day, and if you had like all three of the major textbooks in physics and did ALL the problems and then went though all the schaums outlines, you'd say, hey, that's nothing new, oh wait, this problem looks identical to what i just worked out... etc etc

----

one reason the texts were so good, people realized they had one shot to make it, and proof read it, so there weren't any mistakes or typos... now people just seem to rush it, and new editions seem like half hearted rewrites that often create more errors and errata.

some of the great books, the new edition was something with 4 new chapters at the end, and 99% of the text wasn't tampered with, just new problems.

occasionally people will totally tighten up one or two chapters, or merge them... or break one big chapter into two.

but i liked textbooks where there wasnt a lot of editions, or dramatic changes through the editions...

one of the bothersome things, was something like an electromagnetics text, where, each edition had radically different problems, and if you had like 3 or 4 of the major editions, you got the 'whole' story. Where you don't get that with Halliday and Resnick or Symon or Courant. They dump the whole BRICK on you.

I remember looking at the 60s Courant and John, and thinking, how incredibly hard this gold brick is, but yet there's something really attractive here with it going over the top, and going into stuff that no other calculus text does, but it feels like 8 times the effort to get through a chapter.

Yet, it took years before i found a courant, and i found a 50s blackie edition of that interscience classic. a few years later i found a second copy but it was only one of the two books, orphaned, and i still didnt see courant and john outside of a library...

and they feel totally different in the beginning...kiokemeister - don't know that one

johnson and kiokemeister - 1974 Allyn and Bacon
is that the one?
brown 1978 - 6th edition
goes back to 1960 at least...

lipman bers

228 Calculus - Lipman Bers [and Frank Karal] - Second Edition - Holt Rinehart and Winston 1976
[crystal clear explanations]
[I had come across this book in the university library. Before that I had been getting excellent marks in Calculus by mechanically going thru the rules in my mind. This book changed all that and gave me a proper perspective on the discipline. The explanations are clear and this book is eminently suitable for self study.]
[Recommend this book whole-heartedly at least for the first and second years of calculus. This was about twenty-five years ago! But it's just as relevant now.]
[Barry says Bers was a Russian mathematician emigre to the U.S. who was familiar with Russian textbooks.]
[First Edition] ?
[Second Edition] 1976

m.e.munroe - don't know much about that one

joseph kitchen

88 Calculus of one variable - (Addison-Wesley series in mathematics) - Joseph W Kitchen - Addison-Wesley 1968 - 785 pages
[a superb honors level book - Mathwonk]
[This book is on the level of the ones by spivak, courant, and apostol, and is very modern]
[mathwonk - a nice book - but if the price gets astronomical on the used market then it is absurd to buy it, and that almost anyone of the other good books will give you an enormous amount of education - Fleming or Dieudonne or Courant for cheap is better than an expensive copy of kitchen in the short term]

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outstanding commentary mathwonk...

any other quirky calculus books, from strange disasters to forgotten failures that were pretty cool?

i had the feeling that from 1963 to 1975, you could tell what book was going to be like because of the crazy graphic design...

 

[mathwonk]

http://www.abebooks.com/servlet/SearchResults?an=m.e.munroe&tn=calculusanother quirky but good one: lectures on freshman calculus by cruse and granberg.

i was asked to referee this in 1970, but did not realize the referee report was not supposed to contain any criticism. this is an excellent book, but in my picky way i pointed out the errors in it. i was very upset that the published version did not correct any of the errors i observed. this made me cynical and think that the referee report as a scam.

it did not go far in the market, although it had my favorite quality of carefully and beautifully motivating each main concept. maybe if i had written them a better review it would still be available.

https://www.amazon.com/dp/B002PCY21O/?tag=pfamazon01-20the thing i remember from bers' book was the remark: "calculus is essentially about solving differential equations." i didn't know that, and i appreciated being told that. to me as a student, d.e. was just an annoyingly unenjoyable course i had to take, with tedious solution techniques to memorize and little interesting theory. i didn't realize it is possible to appreciate problems, that have no easy solutions. the problems had not been clearly stated to me. i.e. a d.e. is a vector field. that has beautiful geometry.

 

[RJinkies]

Part I

so the messy part of cruse and granberg was something to do with Decartes' method of tangents on parabolas and how you're only suppossed to cut the curve once?
Was the problem with with complicated functions the tangent might be hitting multiple points with higher degree curves or somethings? [at least that's the gist of the complaint on amazon]. Didnt other textbooks use that method, and fall into similar traps? or it was just something that worked for some equations and not higher degree equations where it could be strange or messy.

[watch out it's sin(x)/x]



- Any thoughts on:
a. Calculus for the Practical Man - JE Thompson [1931/fixed up 1948 - and obsessed with rates and flows]
b. Quick Calculus - Kleppner
[wasnt that late 60s or early 70s, i don't remember if it came out before or after Introduction to Mechanics... but i thought it was a great gesture, all you need with high school algebra is my 'other book' to read 'my other book]

i was pretty skeptical of the need help with calculus textbooks but two textbooks after the 80s seem to be quite good

c. The Calculus Lifesaver: All the Tools You Need to Excel at Calculus - Adrian Banner - Princeton 2007 - 752 pages
[Banner's style is informal, engaging and distinctly non-intimidating, and he takes pains to not skip any steps in discussing a problem. Because of its unique approach, The Calculus Lifesaver is a welcome addition to the arsenal of calculus teaching aids. - MAA]
[I used Adrian Banner's The Calculus Lifesaver as the sole textbook for an intensive, three-week summer Calculus I course for high-school students. I chose this book for several reasons, among them its conversational expository style, its wealth of worked-out examples, and its price. This book is designed to supplement any standard calculus textbook, thus my students will be able to use it again when they take later calculus courses. The students in my class came from diverse backgrounds, ranging from those who had already seen much of the material to others who were struggling with basic algebra. They all uniformly praised the book for being one of the clearest mathematics texts they have ever read, and because it reviews the required prerequisite material. The numerous worked-out examples are an ideal supplement to the lectures. The only difficulty in using this book as a primary text is the lack of additional exercises in the text. However, there are so many sites and sources for calculus problems that this was not a problem. I would definitely use this book again. - Steven J. Miller, Brown University]
[some wonder about the lack of reinforcement]
[not the best for clarity]
[not always easy to follow]
[for volumes with shell and disks - far more complicated than main textbooks and still leaves out a lot of explanation]

d. How to Ace Calculus

and then there is
e. Calculus - Elliot Gootman - Barron's Educational Series 1997 - 342 pages
[said to be much better than the dummies book]
[and for some more useful than the how to ace book]
[how they do it - 'Once you master about twenty basic procedures, the rest becomes far more approachable. I recommend this book highly to those frustrated with standard textbooks or simply wishing to understand the basics of how calculus works.']

f. The Humongous Book of Calculus Problems: For People Who Don't Speak Math - W. Michael Kelley - Alpha 2007 - 576 pages
[Kelley does a great job of stripping away the gobbledygook and delivering you the nuts and bolts of calculus ON PAR with the "hardcore texts". There are many of those "hardcore" books, and they just don't teach well. What this author has done is to teach you how to solve the problems as well as the underlying logic.]

two older super-obscure classics that i found fascinating opinions on:

g. Calculus - Fadell - early 60s
[considered one of the neater post Sputnik calculus books]
[The best may be the book by Fadell also written in the early 60's which has some fantastic figures and a very unique treatment of calculus]

h. Differential and integral calculus - James Ronald Fraser Kent
[verbose older calc text]
[I picked up a used copy of this text based on the five star review that was given. I think this book proves that all of first year calculus can be covered in a compact book. It assumes the reader has mastered pre-calc math and does not waste time covering much of the pre-req material. However, this book still packs a maximum density of information given its size.]
[The Book is less than half the size of the prototype modern calc text.]
[The text is very wordy and broken down into compact subsections. At points, I felt the author could have done a better job explaining certain topics wi th less words and a few more equations. The figures are also not as good as in other older texts like Fobes or early editions of Thomas. However, this book is still much better than most of the calc books in print today. All in all a very decent older text that is worth digging up if you are into calculus pedagogy.]

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eek

i. Calculus and Pizza: A Cookbook for the Hungry Mind - Clifford A. Pickover - Wiley 2003 - 208 pages
[A must see for 9th and 10th grade high school students]
[one word this book is: Enthusiasm]
[This book is the simple solution to every young student avoiding complications in calculus later in life. I was given this book early on during basic algebra (which I wasn't great at). When I finished reading this book I didn't claim to know calculus: I skimmed the first couple chapters over and over. But, I had an idea of what people meant when they said "Calculus."]
[America's public educational systems lack the rigor that is required by its universities and colleges because students are not getting "very basic" ideas early on. This book is a definitive solution. Reading parts of this book in 9th or 10th grade can give students time to let the fundamental simplicity of calculus percolate, something that cannot be rushed in a semester.]
[Students don't need trigonometry, or advanced algebra. They need insight early on. If you're searching for a calculus book because you're having trouble with it now, do your younger friends a favor and recommend this book. It could mean the difference between success and failure when they transition from Precalculus to calculus. This book should be treated the same way astronomy and science survey books are written to inspire interest in young people. Move over earth, life, and health sciences and make some room for Calculus and Pizza - food for the hungry mind.]
[This book served to demistify the entire basics of the calculus for me. Without it, I'd still be wondering about the derivative, or about limits or integrals. On the other hand, it contains about 5% of the stuff in a real calc book, which is why I'm glad I've got both. Even today I refer back to this when the definitions Swokowski gives me are too obscure to understand.]
[If you have trouble understanding calculus, buy this, not a copy of Schaum's outlines. This will open you up to fundamental concepts, and once you have those down, reading any normal calculus text will be a breeze.]
[A really fun read, and you learn Calculus too]
[From the first couple of pages I felt as though I had been thrown in the deep end of the pool in order to learn how to swim. I was anticipating a more accessible book and I was disappointed. The examples of tomato sauce mold, rocket launched meatballs and giant pepperoni (don't ask) didn't serve to ground calculus in the real world for me. Again, maybe a terrific text for people that already have a grounding in the subject, but hardly as comforting as the title would lead you to believe.]

[Yeah, I'm probably the first person to bring up a book called calculus and pizza, but if it is a book that can teach someone calculus 4 years before most people encounter it in school, that's a good thing]

[I recall some book in a 1970 Edmund Scientic Catalogue that had some package or book [i think it was like a book with extra demo materials like cardboard cutouts or something] and the blurb was about how elementary school children could be taught ideas that are in calculus, and i thought that this pizza book is doing similar stuff, and well books that do this sort of thing are rarer than hen's teeth]

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the best newer textbook [yeah another Addison-Wesley book, how creepy is that... as i said they always put out good stuff]

j. Multivariable Calculus - William L. Briggs and Lyle Cochran - Addison Wesley 2010 - 656 pages
[used at UCLA]
[Most readable calculus book I've yet to come across]
[I was re-taking multivariable calculus this past semester (as kind of a filler class at the community college. I just had some general ed. class to take, so I thought I'd try calc III again and see if I would actually learn anything about vector calculus this time around). We were loaned out the paperback Multivariable edition of the Briggs/Cochran calculus book. One down-side of these copies - the ink smudged way too easily. But that's really not a factor in my four-star rating, I promise. ]
[I've managed to take long enough getting through school (as I mostly just take evening and online classes, what with working during the day) that I've used three different calculus books - Stewart, Thomas and now Briggs. Also, a friend and I are kinda math/physics junkies so we both have fairly extensive collections of Dover books and other various textbooks. Point being, I've come across a lot of different calculus books.]
[And this one has just become my favorite. It never feels dumbed-down (like Stewart did), and it's significantly more readable than Thomas calculus (which does Ok at times, then falls apart at other times). If you've happened to used the Knight physics textbook recently, the Briggs/Cochran book is similar in flavor - conversational yet extremely thorough. It still requires focused reading and plenty of practice, but at least the book won't be an obstacle to learning - as is the case with so many other textbooks in the math/physics world, I find.]
[Drawing on their decades of teaching experience, William Briggs and Lyle Cochran have created a calculus text that carries the teacher’s voice beyond the classroom. That voice–evident in the narrative, the figures, and the questions interspersed in the narrative–is a master teacher leading readers to deeper levels of understanding. The authors appeal to readers’ geometric intuition to introduce fundamental concepts and lay the foundation for the more rigorous development that follows. Comprehensive exercise sets have received praise for their creativity, quality, and scope.]

[Though I was a little skeptical about a first edition, my skepticism faded quickly after reading through the beginning of the book, particularly limits. Very, very good explanations and examples that thoroughly prepare the reader for the upcoming exercises. The definitions are great, and the graphics are very well laid out and explained. All in all, though I haven't read through the etire book yet, I have read enough Calculus books to know a good one from a bad one. This being a very good one.]
[Will never be as popular as Stewart's Calculus, and it is far from being a serious, self-respecting Calculus book - such as the one written by Apostol. Not a good text-book for students in Science and Engineering who need to have a better understanding of Calculus and applications, based on more serious Engineering and Physics-born examples, with more serious computations and proofs!]
[This book is actually pretty good, good for self study. But if you want a really good book, I would recommend Ron Larson's Calculus book instead.]
[The book would be great for a high school student who is trying out Calculus, but is not good at Math at all. It may be good for the Liberal Art student pursuing multidisciplinary studies: that is, a mixed salad of Humanities, Education, Social Sciences and Life Sciences, spiced up with some Calculus just for the sake of sounding like a true intellectual!]

[it's got some moody blue and black artwork on it too]

-----

k. Jerrold E. Marsden and Alan Weinstein - Calculus I, II, III - Springer-Verlag [came out in the late 70s or early 80s] second edition is 1985 is all i know about it.. and it was used at Berkeley, since i think Marsden is there and cranks out 3-4 textbooks through the decades...

I heard extremely little about it, any ideas on when it first came out, and how the different editions are, by anyone out there?
Im sure people didnt like 3 orangey yellow textbooks with 3 study guides and then you possibly get pushed into marsden's vector calculus textbook afterwards...

heck here is a neglected text these days from the 60s

l. What Is Calculus About? (New Mathematical Library) - W. W. Sawyer
[someone should talk about one of the first NML books, i thought they were one of the greatest ideas around, a huge series of books to supplement you from high school on up]
[i think the closest anyone came to something sort of like that might be the oxford chemistry series that had all these strange silver and back thin 80s paperbacks which were like 50-70 titles i think...]

[physics only had the anchor science series for teenagers, and man those arent easy to see, but you could always see a few in the bookstores of the 70s, usually the electronics book or some of the history books] It looked like so much promise in the 60s and it petered out in the 70s with the PSSC texts [or likely nixon gutting the libraries and education funding stuff that got pushed 1960-1968]

-----

another newish one that looks good

m. Calculus: The Elements - Michael Comenetz
[Best Textbook on Calculus - Concise & Fun to Read & Comprehensive]
[It's no doubt that Stewart's book is the most popular textbook on Calculus. It's comprehensive and standard. However, it's a pain to read through every page and do all the exercises.]
[In that regard, I've found Michael Comenetz 'Calculus: the Elements' most suitable for students without a solid background who intend to major in physics, math, chemistry, and engineering. Comenetz' book is not only comprehensive but very concisely written. Problems are well chosen - unlike Stewart's that has repetitive/similar problems all over the textbook. Yet, my advice would be 'keep Stewart's as a reference while learn from Comenetz's' This, based on my own experience, is the most effective to achieve high scores in tests and excellent grades.]

 

[RJinkies]

Part II

off topic but a 'friendly' book as in the rudin path to math texts

n. Advanced Calculus: A Friendly Approach - Witold A.J. Kosmala - Prentice-Hall - 700 pages - 1998
[I have copies of Rudin, Apostol, Bear, Fulks, and Protter, but this book beats them all as an introductory text. If you are looking for a self-study text, or if you want a reference companion to help you understand Rudin or Apostol, try this book first. You won't be disappointed.]
[The author of this book has used " a friendly approach " to present the stuff so that readers will actively be engaged in learning with less strain. This has not in a sense simplified the difficult elements of Calculus but bringing along the readers to think and reason while studying the subject.]
[Designed to be readable and intimidation-free, this advanced calculus book presents material that flows logically allowing readers to grasp concepts and proofs. Providing in-depth discussion of topics, the book also features common errors to encourage caution and easy recall of errors. It also presents many proofs in great detail and those which should not provide difficulty are either short or simply outlined. Throughout the book, there are a number of important and useful features, such as cross-referenced functions, expressions, and ideas; footnotes which place mathematical development in historical perspective; an index of symbols; and definitions and theorems which are clearly stated and well marked. An important reference for every professional who uses advanced math.]

For the last huff, jump in anyone...

o. Calculus With Analytic Geometry - 9th edition 2008 now...
[Ron Larson and Edwards] or [Larson, Hosteller and Edwards] - DC Heath and Brooks/Cole

people think the highest and lowest of this textbook, though it's been through a hell of a lot of editions, and i think in the 80s it flaked out with some computer gunk and then went back to basics...

the comments are all over the place *grin*[this isn't Edwards and Penney]
[liked by Alexander Shaumyan - New Haven, CT]
[easy to follow]
[it doesn't really explain things adequately]
[it skips too many steps in the examples]
[some think it's got a nice format and easy to follow]
[too software fixated with frills and fluff and fad though]
[Excellent treatise of 3-semester calculus. A classic]
[Decent text but by no means excellent - 3 out of 5 rating]
[if people complain this book makes calculus too simple, so what? If you are struggling and can't do the easy stuff, then how on Earth are you going to start doing the hard stuff later on?]
[i get the feeling this book isn't better than Sherman Stein's or Thomas and Finney really]
[starts off simple, but then goes into too many shallow applications, with skimpy second year stuff]
[I have many of the same criticisms of this book as I do of the Stewart, although I do think this book does a slightly better job in the very beginning, for example, when introducing the limit, and also in that it leaves out some of the extraneous and confusing attempts at applications in the first chapter. I still think the book contains too many confusing applications from the second chapter onward. I do think the book would be improved by having a completely separate section covering the definition of the limit, however.]
[I like the prose in the examples. I like the presentation of some of the material from multivariable calculus. But again, this book is like a typical intro calc book - it's not rigorous enough, has too much brute force, too many applications, not enough mathematics, not enough creativity. This book doesn't cultivate the awe and wonder that should be present when a student learns calculus.]
[There is no text, in my opinion, more suited towards use in any introductory Calculus series, but this text is also ideal for self-study. The theory is presented in crystal clear fashion, and then multiple examples are given in order of increasing complexity.]
[just another junk book]
[This book does provide the concepts and theory critical to an understanding of calculus. Unfortunately, it is in a wordy, technical, abstract, and thoroughly annoying format. I used this book for calculus 1 and 2. However, unlike my classmates, I learned all the material from an engineering math book (kenneth stroud, engineering mathematics).This book gives you plenty of abstract proofs that look like bull@!#t, but falls far short of my engineering book in encouraging an understanding of calculus. The truth is, this book gives you hundreds of formulas to memorize, instead of a relative few like my engineering book that can cover every problem. Most importantly, I can create these formulas if I need to, because I actually UNDERSTAND what is going on. By the way, I got an A+ in both courses, and I never bothered to learn the epsilon delta crap.]

i ain't got much of a timeline on the book but i got this much
[First Edition]
[Second Edition]
[Third Edition] [started to use computer generated graphs - ugh]
[Fourth Edition] 1993 [started to use computers and graphing calculators - ugh]
[Fifth Edition] [started to use a CD Rom - ugh]
[Sixth Edition] 1998 - 1316 pages [started to do stuff online - ugh]
[Seventh Edition]
[Eighth Edition] 2005 - 1328 pages - Brooks/Cole
[Ninth Edition] 2009 - 1328 pages - now just Larson and Edwards

oh one more

p1 and p2. Lang's simple and non scary calculus text, came out in like 1964 for a basic course, and through the changes in curriculum people found that it's still useful today...

p1. A First Course in Calculus - First edition - Lang - Springer 1964 - 264 pages
[reissued in the past decade as - Short Calculus - yeah the first edition is back]

p2. A First Course in Calculus - fifth edition - Lang - Springer 1998 -752 pages
[the bloated new editions]

the comments:
[simple, but not unsophisticated]
[As a high school teacher, I used this text with great success several times for both AP Calculus BC and AP Calculus AB courses. It is my favorite calculus text to teach from, because it is very user-friendly and the material is presented in such an eloquent way. There are no gratuitous color pictures of people parachuting out of airplanes here. Opening this book is like entering a temple: all is quiet and serene. Epsilon-delta is banished to an appendix, where (in my opinion) it belongs, but all of the proofs are there, and they're presented in a simple (but not unsophisticated) way, with a minimum of unnecessary jargon or obtuse notation. He doesn't belabor the concept of "limit"; most calculus books beat this intuitively obvious concept into the ground. Even though it doesn't cover all of the topics on the AP syllabus, I would rather supplement and use this text rather than any other. - B. Jacobs]
[Calculus for beginning college students]
[I needed to bring my high school calculus up to speed for first year physics studies and found this to be the only book which covered the necessary ground. The material is presented in a thorough manner with the great majority of topics shown with proofs. The book is very well organized and there are abundant worked examples. Some problems are offered which deal with matters not covered in the text, but usually there is a worked example given among the answers. Lang deals with the material in a clear fashion so that the subject matter is usually not difficult to follow.]
[On the negative side I can say that there is no human touch between the covers. His sole attempt at humor is an item following a list of problems in which he notes "relax". In the foreword he exhibits his firm belief that many freshmen arrive unprepared for college calculus, which may be true. But nowhere in the book is there a note of encouragement, so it cannot be described as reader friendly. Finally the index is pathetic - just three pages for a book of 624 pages, so that finding things can be frustrating.]
[Effectively conveys key concepts and skills]
[Serge Lang's text does an effective job of teaching you the skills you need to solve challenging calculus problems, while teaching you to think mathematically. The text is principally concerned with how to solve calculus problems. Key concepts are explained clearly. Methods of solution are effectively demonstrated through examples. The challenging exercises reinforce the concepts, while enabling you to develop the skills required to solve hard problems. Answers to the majority of exercises (not just the odd-numbered ones) are provided in a hundred page appendix, making this text suitable for self-study. In some sections, such as related rates and max-min problems, Lang provides many fully worked out solutions.]
[As effectively as Lang conveys the key concepts and teaches you how to solve problems, he does not neglect the subject's logical development. Topics are introduced only after their logical foundations have been laid. Results are derived. Theorems are proved when Lang feels that they will add to the reader's understanding. Through his exposition and his grouping of logically related exercises, Lang teaches the reader how a mathematician thinks about the subject.]
[The book is divided into five sections: review of basic material, differentiation and elementary functions, integration, Taylor's formula and series, and functions of several variables. The heart of the course is the middle three sections.]
[Most of the topics covered in the review of basic material should be familiar to most readers. However, it is still worth reading since there are challenging problems, properties of the absolute value function are derived from defining the absolute of a number as the square root of the square of the number, conic sections and dilations may be unfamiliar to some readers, and Lang views the material through the prism of a mathematician who knows what concepts are important for understanding higher mathematics.]
[Lang introduces the derivative as the slope of a curve in order to motivate the introduction of the idea of a limit. Next, Lang teaches you techniques of differentiation and shows you how to use them solve applications such as related rate problems. After a detailed discussion of the sine and cosine functions, Lang introduces the Mean Value Theorem and illustrates how it can be used for curve sketching and solving for maxima or minima. Lang covers properties of inverse functions before concluding the section by defining the natural logarithm of x as the area under the curve y = 1/x between 1 and x and defining the exponential function f(x) = e^x as its inverse.]
[The integral is introduced as the area under a curve, with the natural logarithm taken as the motivating example. Lang explains the relationship between integration and differentiation before introducing techniques of integration and their applications. Integration with respect to polar and parametric coordinates is introduced to expand the range of applications. The exercises introduce additional tricks that enable you to solve integrals that do not succumb to the basic techniques. A table of integrals is included on the inside of the book's front and back covers.]
[Lang's demonstrates the power of differential and integral calculus through his discussion of approximation of functions through their Taylor polynomials. This chapter should also give you an idea of how your calculator calculates square roots and the values of trigonometric, exponential, and logarithmic functions. The behavior of series, including convergence and divergence tests, concludes the material on single variable calculus.]
[The material on functions of several variables in the final section of the book is covered in somewhat greater detail in Lang's Calculus of Several Variables (Undergraduate Texts in Mathematics). Since the corresponding chapters in that text include additional sections on the cross product, repeated partial derivatives, and further techniques in partial differentiation and an expanded section on functions depending only on their distance from the origin, I chose to read these chapters in Lang's multi-variable calculus text. The material that is included here, on vectors, differentiation of vectors, and partial differentiation, should give the reader a solid foundation for a course in multi-variable calculus.]
[I have some caveats. There are numerous errors, including some in the answer key. Some terminology is nonstandard, notably the use of bending up (down) for concave up (down), or missing, limiting the text's usefulness as a reference. In the chapter on Taylor polynomials, when Lang requests an answer accurate to n decimal places, what he really means is that the error in the answer should be less than 1/10^n, which is not the same thing. At one point, Lang claims that the Extreme Value Theorem, which he leaves unnamed, is obvious. I turned to the more rigorous texts Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition) by Tom M. Apostol and Calculus by Michael Spivak, where I discovered proofs covering one and half pages of text of the Extreme Value Theorem and a preliminary result on which it depends that Lang does not state until an appendix much later in the book. Perhaps Lang meant the Extreme Value Theorem is intuitive. While I found much of the text to be clear, I sometimes found myself turning to Apostol's text for clarification when I read Lang's proofs.]
[Despite my reservations, I think this text is well worth reading. Reading the text and working through the exercises gives you a good understanding of the key concepts and techniques in calculus, enables you to develop strong problem solving skills, prepares you well for more advanced mathematics courses, and gives you a sense of how mathematicians think about the subject. ]
[a book that focuses on the foundation without trying to do too much and it does that very well. self-contained and easy-to-follow, this book promotes understanding of the basics]

mostly recent stuff i packrat into my books for calculus... but i figure that almost any of these books should be worth discussing here, by anyone who's got a copy, used a copy, browsed it in the library, or utterly hates the book...

--------

another thing to talk about, what were the MOST popular textbooks out there 50s or earlier to today?

Thomas and Finney seemed popular [i wonder if that's because it was just enough to make engineering happy, as well as the math majors and the people who just need calculus once]
[I heard the alt editions were better, and what were those, it sounded like all the unreadable fluff and proofs were yanked out, but those only came out in the 60s or 70s, and the alt editions i think had unique numbering]

and i do recall

[i also think the writing of the 9th edition is actually clearer than in thomas original book - mathwonk]

I'm not sure of story, but wasnt the second edition pushed out really quickly for thomas, and I'm wondering if the first edition had problems, or just so much more was written but not fully completed for the first edition, and well, when the book took off, he said, i finally finished the last few chapters which i needed a few more years to finish up... etc etc
stewart i think started to get popular about 1990 or so..what was always surreal is how some older bookstores would just carry stacks and stacks of the 1967-1974 textbooks for calculus, which were all the mainstream, don't take too many chances, write for all audiences, and keep all that formalism, don't make the book too easy, don't make it too eccentric, don't stick in any material if the other top 7 sellers don't include it... and no one would buy them at 10 dollars and you'd see 15 years of dust on them...yet they would be great books for 2 dollars for the store to dump on people who want 'supplementary reading'

i always thought that the super easy books were far better, and the super difficult ones... the books in the middle just were compromised far too much, and lacked any vision...

any why is that no syllabus around tosses a schaum's outline for calculus or physics on the list?

 

[mathwonk]

my perception of a calculus book is partly influenced by when it came out relative to my math education. kleppner i believe was a harvard physics prof who wrote his book after i had taken a spivak style course from john tate at harvard (as spivak also may have), so did not interest me at the time.

gootman is one of my favorite books for struggling students and i have a copy signed by gootman, my long time colleague and a master teacher and analyst.

i liked lang's calculus books and learned how easy and simple riemann integration is from them.i loved comenetz's book, and wrote the initial rave review of that book. unfortunately i gave away my review copy as a prize to a good student. I attach my (edited) review, no longer available on the publisher's website: (see below)
unfortunately for the buyer, the price has increased from under $40 to over $125. Perhaps that is one reason my review has been removed, since it originally contained a grateful comment about the price.i loved the first edition of edwards and penney, two wonderful scholars and teachers and friends of mine, but to my taste the book did not improve through several editions apparently designed to enlarge its audience at the behest of the publisher. it seemed to serve as the model for stewart's book.

schaum's outline series was wonderful in the old days, extensive and good problems, plus brief and useful theoretical summaries; but more recently when i tried to use it in a course, it seemed greatly reduced in quality and usefulness somehow, no longer worth it.

the elementary error in cruse and granberg is the fact that the fermat criterion for a tangent line is not that the polynomial which vanishes where the line meets the curve should have only one root, but that it should have a double root at the given point.

this is easy to check for polynomials where one can always divide (x-a) out from
[f(x)-f(a)]/(x-a) because of the first forced root, and after doing so, simply set x=a to see if there is a second root. the result is as usual that the slope of the tangent line to y = x^n at x=a is na^(n-1).in fact i have experimented using this method to teach derivatives to undergrads, for polynomials. of course more analysis is required for transcendental functions like sin, e^x.i wrote out this result in complete detail for the author and publishers when they commissioned me to review the book prior to publication, but they ignored it. perhaps the authors did not understand it either, but i suspected at the time, the book was already ready to go to print and thy did not care to know its flaws.

i have written this method up completely with examples in the class notes attached to post #6 of this thread:

https://www.physicsforums.com/showthread.php?t=441018

 

[dustbin]

In reponse to RJinkies partI above:

My calculus course is using Briggs this semester. I think it is a pretty good book... but I feel the exercises are too easy. The explanations are good, though. Definitely better than what I've read of Stewart. Actually, my favorite "popular" calc book is Thomas, I think. There are tons of exercises (100+ per section typically); some of which I've found are also in Apostol and Spivak (decent selection of proof problems). However, certainly not as good as Apostol, Spivak, Courant...

I read a while ago a suggestion for Calculus by Kitchen (forget first name) from mathwonk... I happened to see it in a university library today. Looked like a nice book that covers a lot of material most other books do not.

 

[tinylights]

Hi, I wanted to introduce myself. :)

I have recently discovered that math is my calling, and am studying it at a small 2-year college before transferring out next Fall to pursue my BS. I'm taking Calc 1 right now with a Stewart textbook (though due to the earnest recommendations for it all over this site I have ordered Spivak's Calculus as well) and am doing well, though there is a definite change in difficulty level between Pre-Calculus math and Calculus. It's actually quite exciting to me because I remember finding myself so bored in other classes when I could easily predict where my teachers were going with every idea, and the course I am in now is a lot closer to my pace.

Out of curiosity, does anyone know what the best colleges/universities in Florida are for a solid math education? I live nearby UCF so it is my most likely option, but I want to consider others so as to avoid my grad school speaking at me in a new language. And I've heard of a lot of people having issues with UCF's massive enrollment, primarily that of never getting a chance to connect with your professors.

Secondly, I've looked at a lot of grad school programs and they recommend acquiring reading fluency of mathematical texts in French, German or Russian. Which one(s) are most useful to learn, in your experience?

 

[mathwonk]

I "read" French, German, and Russian, well enough to pass a grad school math proficiency test, but only French well enough to actually read a math paper fairly easily.

As far as Russian goes, so few English speakers read it that most big Russian journals are routinely translated into English.

I staggered through a few sections of Riemann's papers in German but even those are at last available in English.

I always thought I could read Serre's clear papers in French, but boy the English version of Algebraic groups and class fields is much easier to get something out of.So while it is recommended to learn these languages, at least french, and less so german, most of us get by quite well in english, occasionally having to struggle through an original language with a dictionary. but even to do that you need to know the basics of the language.

i.e. learn what languages you can, but be aware that you will be able to read almost everything written fairly recently in english. original languages are needed especially for reading some important works from the 19th century and early 20th cent.

e.g. with my weak german, i still have not read the great paper on linear series on algebraic curves, treated purely algebraically, including an early algebraic proof of the riemann roch theorem, by brill and noether.

it was kind of entertaining trying to struggle through a russian textbook on vector spaces (vyektornye prostranstva) when i kept running across the same words (ochevidno shto and silno) over and over, which turned out to mean "obviously" and "clearly"!

 

[symbolipoint]

MATHWONK,

you described your career progress a few times, but not remembering exactly, could you tell us: Did you study anything (Mathematics) while you were a meat-lugger, not in school? Or did you just work your labor job without studying your subject?

 

[mathwonk]

thats a little like asking country joe mcdonald what he remembers about the 60's, and he answers "nothing".

this is not a thread for discussing politics, but that was a great distraction. those were years when we were fighting in vietnam. it was hard to focus on just preparing for a narrow scientific career. the one advance i made in those years was by assisting/grading in honors calculus, i had to read spivak's calculus book, and learned a lot of calc i should have known much earlier.

 

[converting1]

has here been any older mathematicians (30+) who've made any impact on mathematics (if so who)? Reading up on mathematicians it seems as though everyone makes great work in their early twenties then just die down

 

[micromass]

has here been any older mathematicians (30+) who've made any impact on mathematics (if so who)? Reading up on mathematicians it seems as though everyone makes great work in their early twenties then just die down

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list

 

[converting1]

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list

Guess it's never too late then! Thought I had little time left seeing as I'm 17,

thanks

 

[homeomorphic]

has here been any older mathematicians (30+) who've made any impact on mathematics (if so who)?

30 isn't that old. Actually, very few mathematicians today even get to the point where they can make any significant contributions UNTIL they are about that age. The average PhD age is like 27 or 28, and my impression is that postdocs were this extra thing that they had to stick in because a PhD isn't really enough to become a mathematician anymore. So, by the time you are done just getting started, you're that old.

 

[eliya]

30 isn't that old to start or to finish. A lot of mathematicians ``made impact" beyond their 30's. Andrew Wiles, for instance, missed the Fields Medal by a few months.

As a general rule though, don't think about making an impact. Every mathematician who's active and writing papers is changing mathematics, of course, to different extents. To paraphrase Robion Kirby, don't worry about the significance of your mathematical results, worry about being the best mathematician you can be, and the rest will follow.

 

[chiro]

Take a look at George Polya, who started late relative to a lot of others (consider also that mathematics has exploded since 100 years ago) and didn't start studying mathematics:

http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/polya-george.pdf

Born in 1987, got the doctorate in 1912 so got the doctorate at the age of 25 (but please put that into context for mathematics especially probability at that time, and I am not denigrating Polya when I make these statements).

 

[mathwonk]

whether or not you will do important math is not determined by your age, surname, gender, or anything else. It is based on your desire. go for it.

 

[dkotschessaa]

Just turned 36. Still an undergrad. Not giving up. :)

 

[Mariogs379]

@mathwonk,

regardless of what I do re: staying in NYC vs. Brandeis program, I'm going to take some math in the spring semester. Seems like it makes sense, for continuity's sake, to take real analysis II.

Was also thinking Algebra I. Thoughts?

 

[giorgiv19]

Well, I have read some of the posts about textbook recommendations and want to offer an insight of my own:
Normal calculus textbooks? Don't bother. Don't read them, they do more damage, than good. The best thing to do is pick up a Russian Analysis textbook, like Fihtengolz, Zorich or Kydriatsev. They all come in 3 volumes.
Also no textbook is good without exercises. For this the best one by far is Demidoviche's "A Collection of Problems in Analysis".
The other essential thing for mathematics is linear algebra and analytic geometry. Serge Lange has very good book in linear algebra.
But the most important thing is not just studying at a university. You should look for open seminars. These seminars will give you much greater knowledge, than any course ever would.

 

[mathwonk]

thank you for these views which differ from many usually found here, and supplement them nicely!

 

[NegativeDept]

By the way, to my knowledge, the only mathematicians posting regularly on this site are Matt Grime and me. Please correct me on this point, since nothing this general is ever true.

I raise my hand with magnitude $r \in (0,\tfrac{1}{2}]$. I'm a physics PhD student with a math undergrad degree. My thesis is on quantum decoherence, but it consists entirely of equations, simulations, theorems, and other people's data. When asked, I identify as either "applied mathematician" or "theoretical physicist."

Arnol'd, who is a MUCH better mathematician than me, says math is "a branch of physics, that branch where experiments are cheap." At this late date in my career I am trying to learn from him, and have begun pursuing this hint. I have greatly enjoyed teaching differential equations this year in particular, and have found that the silly structure theorems I learned in linear algebra, have as their real use an application to solving linear systems of ode's. I intend to revise my linear algebra notes now to point this out.

I agree! I just wrote a linear-systems-of-ODEs numerical software package which uses silly theorems of linear algebra to beat the hell out of RK4. (The catch: linear systems only. If you're interested, look up "Magnus expansion.") I'm sure my advisor, who has published huge amounts of Arnol'd-related stuff, would also applaud your effort. I suspect we're both working on one of his big long-term goals: show scientists and engineers that Sophus Lie's view of ODEs can be really practical and useful.

 

[Hercuflea]

Is it possible to receive an applied math Ph.D, but do your dissertation in some other area of science or engineering? I am asking because I want to get a solid foundation on some mathematics courses (functional analysis, advanced and numerical linear algebra, ODE's, PDE's, hilbert spaces, several complex variables) at the graduate level, but I would not really have a chance to take all of these courses if I did an engineering Ph.D. However It seems like it would be the best of both worlds if I could go for an applied math Ph.D. and do my dissertation in nuclear fusion which is ultimately my intended research interest, whilst being able to get the solid mathematical background.

Do you know if this is a common thing to do in applied math programs?

 

[QuantumP7]

I just got What Is Mathematics: An Elementary Approach to Ideas and Methods, Second Edition. It's by Richard Courant, Herbert Robbins and revised by Ian Stewart. I'm REALLY looking forward to solidifying my knowledge of the really basic parts of mathematics. Hopefully, it'll answer some questions I have about the fundamental concepts.

 

[Cod]

I just got What Is Mathematics: An Elementary Approach to Ideas and Methods, Second Edition. It's by Richard Courant, Herbert Robbins and revised by Ian Stewart. I'm REALLY looking forward to solidifying my knowledge of the really basic parts of mathematics. Hopefully, it'll answer some questions I have about the fundamental concepts.

A great book you just got. The beauty of it is, its not a book that must be used in order. You can skip around as you see fit in order to meet your goals.

 

[QuantumP7]

A great book you just got. The beauty of it is, its not a book that must be used in order. You can skip around as you see fit in order to meet your goals.

Thanks! I'm really loving this book so far!

 

[analyzer]

Hello, everyone. I am from Ecuador, and plan to study math at Escuela Politécnica Nacional, one of the most prestigious universities in my country. Perhaps it is the best one in math (the one that does the most research in the area, and the one with the more PhDs teaching.)

The program places emphasis on applied math. There are two concentrations: modeling and scientific computing, and statistics and operations research. The following are the links to the department's curricula.

Modeling and scientific computing: http://www.epn.edu.ec/attachments/article/77/MALLA%20CURRICULAR%20ING%20MATEMATICA-MENCION%20MODELIZACION.pdf

Statistics and operations research: http://www.epn.edu.ec/attachments/article/77/MALLA%20CURRICULAR%20ING%20MATEMATICA-MENCION%20ESTADISTICA.pdf

My question is whether I can pursue graduate studies in pure math with any of both curricula.

Also, I have to mention that there are two other universities in my city which offer programs in math. One is too expensive for my parents (I do not meet the requirements for scholarships). Anyway, I post the link to its math department curriculum:

http://www.usfq.edu.ec/programas_academicos/colegios/politecnico/carreras/Paginas/matematicas.aspx

Do you think it is better preparation for a PhD in pure math?

The other university's program is the following:

http://www.uce.edu.ec/documents/22800/143833/Malla%20Curricular?version=1.0&t=1351174886263

 

[analyzer]

Sorry. The expensive university's math curriculum is actually at the following link:

http://www.usfq.edu.ec/programas_ac...ments/mallas_academicas/malla_matematicas.pdf

 

[SirIsaac]

"i loved comenetz's book, and wrote the initial rave review of that book. unfortunately i gave away my review copy as a prize to a good student. I attach my (edited) review, no longer available on the publisher's website: (see below)
unfortunately for the buyer, the price has increased from under $40 to over $125. Perhaps that is one reason my review has been removed, since it originally contained a grateful comment about the price."

Correction: mathwonk's review is now at
http://www.worldscientific.com/page/4920-review01
and the paperback edition is $67 at Amazon

 

[converting1]

after doing maths straight for around ~5 hours I find I tend to make a lot of mistakes and usually need a break. What do you guys usually do for a break? I can't find anything to do that isn't too distracting, I don't really play video games nor watch television and work out 5 times a week already. I tried to read but again, it just is too distracting. So what should I do for a break? Or a better question, what can I do so I won't need to have a break?

 

[ovael]

“All human evil comes from a single cause, man's inability to sit still in a room.”
-Blaise Pascal

You could also lie down if you have a bed or sofa available. Perhaps even take a nap. Or take a little walk outside.

 

[mathwonk]

i usually walk around the block and then get back at it. short exercise breaks like that are quite helpful, and better than no breaks at all.

 

[n10Newton]

Mathwonk can you give yours Mathematics Department Undergraduate Course Syllabus.and Books used in each semester. There is syllabus given by you but that is of 2006.