Good “casual” advanced math books
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I understand this is likely to be closed as off-topic, but I thought I would give it a try regardless.
I'm curious if there are any good math books out there that take a "casual approach" to higher level topics. I'm very interested in advanced math, but have lost the time as of late to study textbooks rigorously, and I find them too dense to parse casually.
By "casual", I mean something that goes over maybe the history of a certain field and its implications in math and society, going over how it grew and what important contributions occurred at different points. Perhaps even going over the abstract meaning of famous results in the field, or high level overviews of proofs and their innovations. Conversations between mathematicians at the time, stories about how proofs came to be, etc.
I suppose the best place to start would be math history books, but I was curious what else there may be. Are there any good books out there like this? What are your recommendations?
soft-question big-list textbook-recommendation books
$endgroup$
|
show 3 more comments
$begingroup$
I understand this is likely to be closed as off-topic, but I thought I would give it a try regardless.
I'm curious if there are any good math books out there that take a "casual approach" to higher level topics. I'm very interested in advanced math, but have lost the time as of late to study textbooks rigorously, and I find them too dense to parse casually.
By "casual", I mean something that goes over maybe the history of a certain field and its implications in math and society, going over how it grew and what important contributions occurred at different points. Perhaps even going over the abstract meaning of famous results in the field, or high level overviews of proofs and their innovations. Conversations between mathematicians at the time, stories about how proofs came to be, etc.
I suppose the best place to start would be math history books, but I was curious what else there may be. Are there any good books out there like this? What are your recommendations?
soft-question big-list textbook-recommendation books
$endgroup$
3
$begingroup$
Dieudonne has a few maths history books on algebraic geometry and algebraic geometry, which explain the context in which these fields developed. The Grothendieck-Serre correspondence contains an exchange of letters of who might be the most influential postwar mathematicians. Villani has his book "the birth of a theorem" or something like that.
$endgroup$
– Mere Scribe
9 hours ago
1
$begingroup$
This is not history of mathematics, and I don't know if the material can be considered "advanced" in any sense but looks fun: bookstore.ams.org/mbk-46
$endgroup$
– Qfwfq
9 hours ago
1
$begingroup$
I really liked Love & Math by Edward Frenkel.
$endgroup$
– Fred Rohrer
9 hours ago
1
$begingroup$
I really enjoyed History of Topology by I.M. James. It's a very casual read, but walks you through a lot of "advanced" mathematics.
$endgroup$
– yousuf soliman
7 hours ago
1
$begingroup$
Not a book, but the ICM surveys (impa.br/icm2018) are often great for getting a very basic idea of what's going on in various fields outside of one's own.
$endgroup$
– Sam Hopkins
3 hours ago
|
show 3 more comments
$begingroup$
I understand this is likely to be closed as off-topic, but I thought I would give it a try regardless.
I'm curious if there are any good math books out there that take a "casual approach" to higher level topics. I'm very interested in advanced math, but have lost the time as of late to study textbooks rigorously, and I find them too dense to parse casually.
By "casual", I mean something that goes over maybe the history of a certain field and its implications in math and society, going over how it grew and what important contributions occurred at different points. Perhaps even going over the abstract meaning of famous results in the field, or high level overviews of proofs and their innovations. Conversations between mathematicians at the time, stories about how proofs came to be, etc.
I suppose the best place to start would be math history books, but I was curious what else there may be. Are there any good books out there like this? What are your recommendations?
soft-question big-list textbook-recommendation books
$endgroup$
I understand this is likely to be closed as off-topic, but I thought I would give it a try regardless.
I'm curious if there are any good math books out there that take a "casual approach" to higher level topics. I'm very interested in advanced math, but have lost the time as of late to study textbooks rigorously, and I find them too dense to parse casually.
By "casual", I mean something that goes over maybe the history of a certain field and its implications in math and society, going over how it grew and what important contributions occurred at different points. Perhaps even going over the abstract meaning of famous results in the field, or high level overviews of proofs and their innovations. Conversations between mathematicians at the time, stories about how proofs came to be, etc.
I suppose the best place to start would be math history books, but I was curious what else there may be. Are there any good books out there like this? What are your recommendations?
soft-question big-list textbook-recommendation books
soft-question big-list textbook-recommendation books
edited 6 hours ago
community wiki
user3002473
3
$begingroup$
Dieudonne has a few maths history books on algebraic geometry and algebraic geometry, which explain the context in which these fields developed. The Grothendieck-Serre correspondence contains an exchange of letters of who might be the most influential postwar mathematicians. Villani has his book "the birth of a theorem" or something like that.
$endgroup$
– Mere Scribe
9 hours ago
1
$begingroup$
This is not history of mathematics, and I don't know if the material can be considered "advanced" in any sense but looks fun: bookstore.ams.org/mbk-46
$endgroup$
– Qfwfq
9 hours ago
1
$begingroup$
I really liked Love & Math by Edward Frenkel.
$endgroup$
– Fred Rohrer
9 hours ago
1
$begingroup$
I really enjoyed History of Topology by I.M. James. It's a very casual read, but walks you through a lot of "advanced" mathematics.
$endgroup$
– yousuf soliman
7 hours ago
1
$begingroup$
Not a book, but the ICM surveys (impa.br/icm2018) are often great for getting a very basic idea of what's going on in various fields outside of one's own.
$endgroup$
– Sam Hopkins
3 hours ago
|
show 3 more comments
3
$begingroup$
Dieudonne has a few maths history books on algebraic geometry and algebraic geometry, which explain the context in which these fields developed. The Grothendieck-Serre correspondence contains an exchange of letters of who might be the most influential postwar mathematicians. Villani has his book "the birth of a theorem" or something like that.
$endgroup$
– Mere Scribe
9 hours ago
1
$begingroup$
This is not history of mathematics, and I don't know if the material can be considered "advanced" in any sense but looks fun: bookstore.ams.org/mbk-46
$endgroup$
– Qfwfq
9 hours ago
1
$begingroup$
I really liked Love & Math by Edward Frenkel.
$endgroup$
– Fred Rohrer
9 hours ago
1
$begingroup$
I really enjoyed History of Topology by I.M. James. It's a very casual read, but walks you through a lot of "advanced" mathematics.
$endgroup$
– yousuf soliman
7 hours ago
1
$begingroup$
Not a book, but the ICM surveys (impa.br/icm2018) are often great for getting a very basic idea of what's going on in various fields outside of one's own.
$endgroup$
– Sam Hopkins
3 hours ago
3
3
$begingroup$
Dieudonne has a few maths history books on algebraic geometry and algebraic geometry, which explain the context in which these fields developed. The Grothendieck-Serre correspondence contains an exchange of letters of who might be the most influential postwar mathematicians. Villani has his book "the birth of a theorem" or something like that.
$endgroup$
– Mere Scribe
9 hours ago
$begingroup$
Dieudonne has a few maths history books on algebraic geometry and algebraic geometry, which explain the context in which these fields developed. The Grothendieck-Serre correspondence contains an exchange of letters of who might be the most influential postwar mathematicians. Villani has his book "the birth of a theorem" or something like that.
$endgroup$
– Mere Scribe
9 hours ago
1
1
$begingroup$
This is not history of mathematics, and I don't know if the material can be considered "advanced" in any sense but looks fun: bookstore.ams.org/mbk-46
$endgroup$
– Qfwfq
9 hours ago
$begingroup$
This is not history of mathematics, and I don't know if the material can be considered "advanced" in any sense but looks fun: bookstore.ams.org/mbk-46
$endgroup$
– Qfwfq
9 hours ago
1
1
$begingroup$
I really liked Love & Math by Edward Frenkel.
$endgroup$
– Fred Rohrer
9 hours ago
$begingroup$
I really liked Love & Math by Edward Frenkel.
$endgroup$
– Fred Rohrer
9 hours ago
1
1
$begingroup$
I really enjoyed History of Topology by I.M. James. It's a very casual read, but walks you through a lot of "advanced" mathematics.
$endgroup$
– yousuf soliman
7 hours ago
$begingroup$
I really enjoyed History of Topology by I.M. James. It's a very casual read, but walks you through a lot of "advanced" mathematics.
$endgroup$
– yousuf soliman
7 hours ago
1
1
$begingroup$
Not a book, but the ICM surveys (impa.br/icm2018) are often great for getting a very basic idea of what's going on in various fields outside of one's own.
$endgroup$
– Sam Hopkins
3 hours ago
$begingroup$
Not a book, but the ICM surveys (impa.br/icm2018) are often great for getting a very basic idea of what's going on in various fields outside of one's own.
$endgroup$
– Sam Hopkins
3 hours ago
|
show 3 more comments
12 Answers
12
active
oldest
votes
$begingroup$
What's one person's "higher level topics" is another person's "elementary math", so you should be more specific about the desired level.
But still you may try these books:
Michio Kuga, Galois' dream,
David Mumford, Caroline Series, David Wright, Indra's Pearls,
Hermann Weyl, Symmetry.
Marcel Berger, Geometry revealed,
D. Hilbert and Cohn-Vossen, Geometry and imagination,
T. W. Korner, Fourier Analysis,
T. W. Korner, The pleasures of counting.
A. A. Kirillov, What are numbers?
V. Arnold, Huygens and Barrow, Newton and Hooke.
Mark Levi, Classical mechanics with Calculus of variations
and optimal control.Shlomo Sternberg, Group theory and physics,
Shlomo Sternberg, Celestial mechanics.
All these books are written in a leisurely informal style, with a lot of
side remarks and historical comments, and almost no prerequisites. But the level of sophistication varies widely. Also don't miss:
Roger Penrose, The road to reality. A complete guide to the laws of the universe. It is on physics, but contains a lot of mathematics).
$endgroup$
$begingroup$
Kirillov's is "What are numbers?"
$endgroup$
– Amir Asghari
6 hours ago
1
$begingroup$
To the reader: the title of Kuga's book might be misleading: the book is not about classical Galois theory (as one might expect), but about some of its more recent extensions, such as fundamental groups of covering spaces or differential Galois theory.
$endgroup$
– Alex M.
6 hours ago
$begingroup$
@Amir Asghari: thanks for the correction. I only have the Russian original.
$endgroup$
– Alexandre Eremenko
1 hour ago
$begingroup$
@Alex M. It is not about Galois theory. It is about Galois dream. About the theory he wanted to create (as we know from his letters).
$endgroup$
– Alexandre Eremenko
1 hour ago
add a comment |
$begingroup$
Elementary Applied Topology by Ghrist does a fantastic job surveying recent trends in the application of (co)homological methods to practical science and engineering. It goes all the way from Euler characteristic to sheaf cohomology.
Oh, and the illustrations, depending on how far you get with deciphering them, are pretty cool too:
$endgroup$
add a comment |
$begingroup$
Birth of a Theorem: A Mathematical Adventure, by Cedric Villani. I've linked to a review.
$endgroup$
add a comment |
$begingroup$
I personally enjoyed The KAM Story by H. Scott Dumas. It gives an overview of the history of KAM theory. Very enjoyable and yet informative.
$endgroup$
add a comment |
$begingroup$
I find the Carus Mathematical Monographs to be in this category.
Also, by Julian Havil - "The Irrationals" and "Exploring Gamma".
$endgroup$
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Many Carus monographs are excellent. MY favorite one is P. Doyle and L. Snell, Random walks and electric networks.
$endgroup$
– Alexandre Eremenko
1 hour ago
add a comment |
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I think that the "Number Theory" series by Kato, Kurokawa, Kurihara and Saito fits here. They are beautifully written and require only some undergradute algebra and analysis. They were published (translated) in the AMS Translations of Mathematical Monographs:
Number theory. 1. Fermat's dream
Number theory. 2. Introduction to class field theory
Number theory. 3. Iwasawa theory and modular forms
$endgroup$
add a comment |
$begingroup$
Regarding differential geometry and topology, there is the 3 volume "A Mathematical Gift - The Interplay Between Topology, Functions, Geometry, and Algebra" by K. Ueno, K. Shiga, S. Morita, T. Sunada. The level is "relaxed undergraduate mathematics". The book attempts to bring to the front the intuition behind some of the concepts encountered in geometry. (All the 4 authors are mathematicians working in Japanese universities.)
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add a comment |
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In 'How to bake a π?', Eugenia Cheng provides a nice view of mathematics in general and category theory in particular that may fit your definition of 'casual'. Either way it is a very nice reading.
$endgroup$
add a comment |
$begingroup$
Silvanus P. Thompson's Calculus Made Easy is a good read. Per the reviews, the paperback and Kindle versions should be avoided in favor of the hardcover, although my softcover copy predates this by 2-3 decades.
$endgroup$
add a comment |
$begingroup$
For a casual and beautiful promenade, there is A Singular Mathematical Promenade by E. Ghys.
For French readers, the collection
Leçons de mathématiques d'aujourd'hui (there are now five volumes) presents a panorama of various subjects and research domains in (mostly pure) mathematics accessible to graduate or advanced undergraduate students.
$endgroup$
add a comment |
$begingroup$
I would add 3 favorites:
The first two (more or less continuing one another) are by W Narkiewicz and are quite comprehensive combining history, some proofs, excellent references and state of the art results up to ~2010:
The Development of Prime Number Theory : From Euclid to Hardy and Littlewood
Rational Number Theory in the 20th Century: From PNT to FLT
Finally a superb exposition with proofs, explanations, history, from D Choimet and H Queffelec:
Twelve Landmarks of Twentieth-Century Analysis
$endgroup$
add a comment |
$begingroup$
For a casual book on cryptography and the mathematics behind it, I'll recommend Simon Singh's 'The Code Book'. The concept of modular mathematics and public key cryptography are explained beautifully.
$endgroup$
add a comment |
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12 Answers
12
active
oldest
votes
12 Answers
12
active
oldest
votes
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oldest
votes
$begingroup$
What's one person's "higher level topics" is another person's "elementary math", so you should be more specific about the desired level.
But still you may try these books:
Michio Kuga, Galois' dream,
David Mumford, Caroline Series, David Wright, Indra's Pearls,
Hermann Weyl, Symmetry.
Marcel Berger, Geometry revealed,
D. Hilbert and Cohn-Vossen, Geometry and imagination,
T. W. Korner, Fourier Analysis,
T. W. Korner, The pleasures of counting.
A. A. Kirillov, What are numbers?
V. Arnold, Huygens and Barrow, Newton and Hooke.
Mark Levi, Classical mechanics with Calculus of variations
and optimal control.Shlomo Sternberg, Group theory and physics,
Shlomo Sternberg, Celestial mechanics.
All these books are written in a leisurely informal style, with a lot of
side remarks and historical comments, and almost no prerequisites. But the level of sophistication varies widely. Also don't miss:
Roger Penrose, The road to reality. A complete guide to the laws of the universe. It is on physics, but contains a lot of mathematics).
$endgroup$
$begingroup$
Kirillov's is "What are numbers?"
$endgroup$
– Amir Asghari
6 hours ago
1
$begingroup$
To the reader: the title of Kuga's book might be misleading: the book is not about classical Galois theory (as one might expect), but about some of its more recent extensions, such as fundamental groups of covering spaces or differential Galois theory.
$endgroup$
– Alex M.
6 hours ago
$begingroup$
@Amir Asghari: thanks for the correction. I only have the Russian original.
$endgroup$
– Alexandre Eremenko
1 hour ago
$begingroup$
@Alex M. It is not about Galois theory. It is about Galois dream. About the theory he wanted to create (as we know from his letters).
$endgroup$
– Alexandre Eremenko
1 hour ago
add a comment |
$begingroup$
What's one person's "higher level topics" is another person's "elementary math", so you should be more specific about the desired level.
But still you may try these books:
Michio Kuga, Galois' dream,
David Mumford, Caroline Series, David Wright, Indra's Pearls,
Hermann Weyl, Symmetry.
Marcel Berger, Geometry revealed,
D. Hilbert and Cohn-Vossen, Geometry and imagination,
T. W. Korner, Fourier Analysis,
T. W. Korner, The pleasures of counting.
A. A. Kirillov, What are numbers?
V. Arnold, Huygens and Barrow, Newton and Hooke.
Mark Levi, Classical mechanics with Calculus of variations
and optimal control.Shlomo Sternberg, Group theory and physics,
Shlomo Sternberg, Celestial mechanics.
All these books are written in a leisurely informal style, with a lot of
side remarks and historical comments, and almost no prerequisites. But the level of sophistication varies widely. Also don't miss:
Roger Penrose, The road to reality. A complete guide to the laws of the universe. It is on physics, but contains a lot of mathematics).
$endgroup$
$begingroup$
Kirillov's is "What are numbers?"
$endgroup$
– Amir Asghari
6 hours ago
1
$begingroup$
To the reader: the title of Kuga's book might be misleading: the book is not about classical Galois theory (as one might expect), but about some of its more recent extensions, such as fundamental groups of covering spaces or differential Galois theory.
$endgroup$
– Alex M.
6 hours ago
$begingroup$
@Amir Asghari: thanks for the correction. I only have the Russian original.
$endgroup$
– Alexandre Eremenko
1 hour ago
$begingroup$
@Alex M. It is not about Galois theory. It is about Galois dream. About the theory he wanted to create (as we know from his letters).
$endgroup$
– Alexandre Eremenko
1 hour ago
add a comment |
$begingroup$
What's one person's "higher level topics" is another person's "elementary math", so you should be more specific about the desired level.
But still you may try these books:
Michio Kuga, Galois' dream,
David Mumford, Caroline Series, David Wright, Indra's Pearls,
Hermann Weyl, Symmetry.
Marcel Berger, Geometry revealed,
D. Hilbert and Cohn-Vossen, Geometry and imagination,
T. W. Korner, Fourier Analysis,
T. W. Korner, The pleasures of counting.
A. A. Kirillov, What are numbers?
V. Arnold, Huygens and Barrow, Newton and Hooke.
Mark Levi, Classical mechanics with Calculus of variations
and optimal control.Shlomo Sternberg, Group theory and physics,
Shlomo Sternberg, Celestial mechanics.
All these books are written in a leisurely informal style, with a lot of
side remarks and historical comments, and almost no prerequisites. But the level of sophistication varies widely. Also don't miss:
Roger Penrose, The road to reality. A complete guide to the laws of the universe. It is on physics, but contains a lot of mathematics).
$endgroup$
What's one person's "higher level topics" is another person's "elementary math", so you should be more specific about the desired level.
But still you may try these books:
Michio Kuga, Galois' dream,
David Mumford, Caroline Series, David Wright, Indra's Pearls,
Hermann Weyl, Symmetry.
Marcel Berger, Geometry revealed,
D. Hilbert and Cohn-Vossen, Geometry and imagination,
T. W. Korner, Fourier Analysis,
T. W. Korner, The pleasures of counting.
A. A. Kirillov, What are numbers?
V. Arnold, Huygens and Barrow, Newton and Hooke.
Mark Levi, Classical mechanics with Calculus of variations
and optimal control.Shlomo Sternberg, Group theory and physics,
Shlomo Sternberg, Celestial mechanics.
All these books are written in a leisurely informal style, with a lot of
side remarks and historical comments, and almost no prerequisites. But the level of sophistication varies widely. Also don't miss:
Roger Penrose, The road to reality. A complete guide to the laws of the universe. It is on physics, but contains a lot of mathematics).
edited 1 hour ago
community wiki
5 revs
Alexandre Eremenko
$begingroup$
Kirillov's is "What are numbers?"
$endgroup$
– Amir Asghari
6 hours ago
1
$begingroup$
To the reader: the title of Kuga's book might be misleading: the book is not about classical Galois theory (as one might expect), but about some of its more recent extensions, such as fundamental groups of covering spaces or differential Galois theory.
$endgroup$
– Alex M.
6 hours ago
$begingroup$
@Amir Asghari: thanks for the correction. I only have the Russian original.
$endgroup$
– Alexandre Eremenko
1 hour ago
$begingroup$
@Alex M. It is not about Galois theory. It is about Galois dream. About the theory he wanted to create (as we know from his letters).
$endgroup$
– Alexandre Eremenko
1 hour ago
add a comment |
$begingroup$
Kirillov's is "What are numbers?"
$endgroup$
– Amir Asghari
6 hours ago
1
$begingroup$
To the reader: the title of Kuga's book might be misleading: the book is not about classical Galois theory (as one might expect), but about some of its more recent extensions, such as fundamental groups of covering spaces or differential Galois theory.
$endgroup$
– Alex M.
6 hours ago
$begingroup$
@Amir Asghari: thanks for the correction. I only have the Russian original.
$endgroup$
– Alexandre Eremenko
1 hour ago
$begingroup$
@Alex M. It is not about Galois theory. It is about Galois dream. About the theory he wanted to create (as we know from his letters).
$endgroup$
– Alexandre Eremenko
1 hour ago
$begingroup$
Kirillov's is "What are numbers?"
$endgroup$
– Amir Asghari
6 hours ago
$begingroup$
Kirillov's is "What are numbers?"
$endgroup$
– Amir Asghari
6 hours ago
1
1
$begingroup$
To the reader: the title of Kuga's book might be misleading: the book is not about classical Galois theory (as one might expect), but about some of its more recent extensions, such as fundamental groups of covering spaces or differential Galois theory.
$endgroup$
– Alex M.
6 hours ago
$begingroup$
To the reader: the title of Kuga's book might be misleading: the book is not about classical Galois theory (as one might expect), but about some of its more recent extensions, such as fundamental groups of covering spaces or differential Galois theory.
$endgroup$
– Alex M.
6 hours ago
$begingroup$
@Amir Asghari: thanks for the correction. I only have the Russian original.
$endgroup$
– Alexandre Eremenko
1 hour ago
$begingroup$
@Amir Asghari: thanks for the correction. I only have the Russian original.
$endgroup$
– Alexandre Eremenko
1 hour ago
$begingroup$
@Alex M. It is not about Galois theory. It is about Galois dream. About the theory he wanted to create (as we know from his letters).
$endgroup$
– Alexandre Eremenko
1 hour ago
$begingroup$
@Alex M. It is not about Galois theory. It is about Galois dream. About the theory he wanted to create (as we know from his letters).
$endgroup$
– Alexandre Eremenko
1 hour ago
add a comment |
$begingroup$
Elementary Applied Topology by Ghrist does a fantastic job surveying recent trends in the application of (co)homological methods to practical science and engineering. It goes all the way from Euler characteristic to sheaf cohomology.
Oh, and the illustrations, depending on how far you get with deciphering them, are pretty cool too:
$endgroup$
add a comment |
$begingroup$
Elementary Applied Topology by Ghrist does a fantastic job surveying recent trends in the application of (co)homological methods to practical science and engineering. It goes all the way from Euler characteristic to sheaf cohomology.
Oh, and the illustrations, depending on how far you get with deciphering them, are pretty cool too:
$endgroup$
add a comment |
$begingroup$
Elementary Applied Topology by Ghrist does a fantastic job surveying recent trends in the application of (co)homological methods to practical science and engineering. It goes all the way from Euler characteristic to sheaf cohomology.
Oh, and the illustrations, depending on how far you get with deciphering them, are pretty cool too:
$endgroup$
Elementary Applied Topology by Ghrist does a fantastic job surveying recent trends in the application of (co)homological methods to practical science and engineering. It goes all the way from Euler characteristic to sheaf cohomology.
Oh, and the illustrations, depending on how far you get with deciphering them, are pretty cool too:
answered 6 hours ago
community wiki
Vidit Nanda
add a comment |
add a comment |
$begingroup$
Birth of a Theorem: A Mathematical Adventure, by Cedric Villani. I've linked to a review.
$endgroup$
add a comment |
$begingroup$
Birth of a Theorem: A Mathematical Adventure, by Cedric Villani. I've linked to a review.
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add a comment |
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Birth of a Theorem: A Mathematical Adventure, by Cedric Villani. I've linked to a review.
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Birth of a Theorem: A Mathematical Adventure, by Cedric Villani. I've linked to a review.
answered 7 hours ago
community wiki
Gerry Myerson
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add a comment |
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I personally enjoyed The KAM Story by H. Scott Dumas. It gives an overview of the history of KAM theory. Very enjoyable and yet informative.
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add a comment |
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I personally enjoyed The KAM Story by H. Scott Dumas. It gives an overview of the history of KAM theory. Very enjoyable and yet informative.
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add a comment |
$begingroup$
I personally enjoyed The KAM Story by H. Scott Dumas. It gives an overview of the history of KAM theory. Very enjoyable and yet informative.
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I personally enjoyed The KAM Story by H. Scott Dumas. It gives an overview of the history of KAM theory. Very enjoyable and yet informative.
answered 7 hours ago
community wiki
Severin Schraven
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I find the Carus Mathematical Monographs to be in this category.
Also, by Julian Havil - "The Irrationals" and "Exploring Gamma".
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Many Carus monographs are excellent. MY favorite one is P. Doyle and L. Snell, Random walks and electric networks.
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– Alexandre Eremenko
1 hour ago
add a comment |
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I find the Carus Mathematical Monographs to be in this category.
Also, by Julian Havil - "The Irrationals" and "Exploring Gamma".
$endgroup$
$begingroup$
Many Carus monographs are excellent. MY favorite one is P. Doyle and L. Snell, Random walks and electric networks.
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– Alexandre Eremenko
1 hour ago
add a comment |
$begingroup$
I find the Carus Mathematical Monographs to be in this category.
Also, by Julian Havil - "The Irrationals" and "Exploring Gamma".
$endgroup$
I find the Carus Mathematical Monographs to be in this category.
Also, by Julian Havil - "The Irrationals" and "Exploring Gamma".
edited 3 hours ago
community wiki
2 revs, 2 users 80%
David Campen
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Many Carus monographs are excellent. MY favorite one is P. Doyle and L. Snell, Random walks and electric networks.
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– Alexandre Eremenko
1 hour ago
add a comment |
$begingroup$
Many Carus monographs are excellent. MY favorite one is P. Doyle and L. Snell, Random walks and electric networks.
$endgroup$
– Alexandre Eremenko
1 hour ago
$begingroup$
Many Carus monographs are excellent. MY favorite one is P. Doyle and L. Snell, Random walks and electric networks.
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– Alexandre Eremenko
1 hour ago
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Many Carus monographs are excellent. MY favorite one is P. Doyle and L. Snell, Random walks and electric networks.
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– Alexandre Eremenko
1 hour ago
add a comment |
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I think that the "Number Theory" series by Kato, Kurokawa, Kurihara and Saito fits here. They are beautifully written and require only some undergradute algebra and analysis. They were published (translated) in the AMS Translations of Mathematical Monographs:
Number theory. 1. Fermat's dream
Number theory. 2. Introduction to class field theory
Number theory. 3. Iwasawa theory and modular forms
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add a comment |
$begingroup$
I think that the "Number Theory" series by Kato, Kurokawa, Kurihara and Saito fits here. They are beautifully written and require only some undergradute algebra and analysis. They were published (translated) in the AMS Translations of Mathematical Monographs:
Number theory. 1. Fermat's dream
Number theory. 2. Introduction to class field theory
Number theory. 3. Iwasawa theory and modular forms
$endgroup$
add a comment |
$begingroup$
I think that the "Number Theory" series by Kato, Kurokawa, Kurihara and Saito fits here. They are beautifully written and require only some undergradute algebra and analysis. They were published (translated) in the AMS Translations of Mathematical Monographs:
Number theory. 1. Fermat's dream
Number theory. 2. Introduction to class field theory
Number theory. 3. Iwasawa theory and modular forms
$endgroup$
I think that the "Number Theory" series by Kato, Kurokawa, Kurihara and Saito fits here. They are beautifully written and require only some undergradute algebra and analysis. They were published (translated) in the AMS Translations of Mathematical Monographs:
Number theory. 1. Fermat's dream
Number theory. 2. Introduction to class field theory
Number theory. 3. Iwasawa theory and modular forms
edited 2 hours ago
community wiki
2 revs, 2 users 95%
EFinat-S
add a comment |
add a comment |
$begingroup$
Regarding differential geometry and topology, there is the 3 volume "A Mathematical Gift - The Interplay Between Topology, Functions, Geometry, and Algebra" by K. Ueno, K. Shiga, S. Morita, T. Sunada. The level is "relaxed undergraduate mathematics". The book attempts to bring to the front the intuition behind some of the concepts encountered in geometry. (All the 4 authors are mathematicians working in Japanese universities.)
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add a comment |
$begingroup$
Regarding differential geometry and topology, there is the 3 volume "A Mathematical Gift - The Interplay Between Topology, Functions, Geometry, and Algebra" by K. Ueno, K. Shiga, S. Morita, T. Sunada. The level is "relaxed undergraduate mathematics". The book attempts to bring to the front the intuition behind some of the concepts encountered in geometry. (All the 4 authors are mathematicians working in Japanese universities.)
$endgroup$
add a comment |
$begingroup$
Regarding differential geometry and topology, there is the 3 volume "A Mathematical Gift - The Interplay Between Topology, Functions, Geometry, and Algebra" by K. Ueno, K. Shiga, S. Morita, T. Sunada. The level is "relaxed undergraduate mathematics". The book attempts to bring to the front the intuition behind some of the concepts encountered in geometry. (All the 4 authors are mathematicians working in Japanese universities.)
$endgroup$
Regarding differential geometry and topology, there is the 3 volume "A Mathematical Gift - The Interplay Between Topology, Functions, Geometry, and Algebra" by K. Ueno, K. Shiga, S. Morita, T. Sunada. The level is "relaxed undergraduate mathematics". The book attempts to bring to the front the intuition behind some of the concepts encountered in geometry. (All the 4 authors are mathematicians working in Japanese universities.)
answered 6 hours ago
community wiki
Alex M.
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In 'How to bake a π?', Eugenia Cheng provides a nice view of mathematics in general and category theory in particular that may fit your definition of 'casual'. Either way it is a very nice reading.
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add a comment |
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In 'How to bake a π?', Eugenia Cheng provides a nice view of mathematics in general and category theory in particular that may fit your definition of 'casual'. Either way it is a very nice reading.
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add a comment |
$begingroup$
In 'How to bake a π?', Eugenia Cheng provides a nice view of mathematics in general and category theory in particular that may fit your definition of 'casual'. Either way it is a very nice reading.
$endgroup$
In 'How to bake a π?', Eugenia Cheng provides a nice view of mathematics in general and category theory in particular that may fit your definition of 'casual'. Either way it is a very nice reading.
answered 6 hours ago
community wiki
Melquíades Ochoa
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add a comment |
$begingroup$
Silvanus P. Thompson's Calculus Made Easy is a good read. Per the reviews, the paperback and Kindle versions should be avoided in favor of the hardcover, although my softcover copy predates this by 2-3 decades.
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add a comment |
$begingroup$
Silvanus P. Thompson's Calculus Made Easy is a good read. Per the reviews, the paperback and Kindle versions should be avoided in favor of the hardcover, although my softcover copy predates this by 2-3 decades.
$endgroup$
add a comment |
$begingroup$
Silvanus P. Thompson's Calculus Made Easy is a good read. Per the reviews, the paperback and Kindle versions should be avoided in favor of the hardcover, although my softcover copy predates this by 2-3 decades.
$endgroup$
Silvanus P. Thompson's Calculus Made Easy is a good read. Per the reviews, the paperback and Kindle versions should be avoided in favor of the hardcover, although my softcover copy predates this by 2-3 decades.
answered 1 hour ago
community wiki
Crayoneater
add a comment |
add a comment |
$begingroup$
For a casual and beautiful promenade, there is A Singular Mathematical Promenade by E. Ghys.
For French readers, the collection
Leçons de mathématiques d'aujourd'hui (there are now five volumes) presents a panorama of various subjects and research domains in (mostly pure) mathematics accessible to graduate or advanced undergraduate students.
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add a comment |
$begingroup$
For a casual and beautiful promenade, there is A Singular Mathematical Promenade by E. Ghys.
For French readers, the collection
Leçons de mathématiques d'aujourd'hui (there are now five volumes) presents a panorama of various subjects and research domains in (mostly pure) mathematics accessible to graduate or advanced undergraduate students.
$endgroup$
add a comment |
$begingroup$
For a casual and beautiful promenade, there is A Singular Mathematical Promenade by E. Ghys.
For French readers, the collection
Leçons de mathématiques d'aujourd'hui (there are now five volumes) presents a panorama of various subjects and research domains in (mostly pure) mathematics accessible to graduate or advanced undergraduate students.
$endgroup$
For a casual and beautiful promenade, there is A Singular Mathematical Promenade by E. Ghys.
For French readers, the collection
Leçons de mathématiques d'aujourd'hui (there are now five volumes) presents a panorama of various subjects and research domains in (mostly pure) mathematics accessible to graduate or advanced undergraduate students.
answered 43 mins ago
community wiki
HYL
add a comment |
add a comment |
$begingroup$
I would add 3 favorites:
The first two (more or less continuing one another) are by W Narkiewicz and are quite comprehensive combining history, some proofs, excellent references and state of the art results up to ~2010:
The Development of Prime Number Theory : From Euclid to Hardy and Littlewood
Rational Number Theory in the 20th Century: From PNT to FLT
Finally a superb exposition with proofs, explanations, history, from D Choimet and H Queffelec:
Twelve Landmarks of Twentieth-Century Analysis
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add a comment |
$begingroup$
I would add 3 favorites:
The first two (more or less continuing one another) are by W Narkiewicz and are quite comprehensive combining history, some proofs, excellent references and state of the art results up to ~2010:
The Development of Prime Number Theory : From Euclid to Hardy and Littlewood
Rational Number Theory in the 20th Century: From PNT to FLT
Finally a superb exposition with proofs, explanations, history, from D Choimet and H Queffelec:
Twelve Landmarks of Twentieth-Century Analysis
$endgroup$
add a comment |
$begingroup$
I would add 3 favorites:
The first two (more or less continuing one another) are by W Narkiewicz and are quite comprehensive combining history, some proofs, excellent references and state of the art results up to ~2010:
The Development of Prime Number Theory : From Euclid to Hardy and Littlewood
Rational Number Theory in the 20th Century: From PNT to FLT
Finally a superb exposition with proofs, explanations, history, from D Choimet and H Queffelec:
Twelve Landmarks of Twentieth-Century Analysis
$endgroup$
I would add 3 favorites:
The first two (more or less continuing one another) are by W Narkiewicz and are quite comprehensive combining history, some proofs, excellent references and state of the art results up to ~2010:
The Development of Prime Number Theory : From Euclid to Hardy and Littlewood
Rational Number Theory in the 20th Century: From PNT to FLT
Finally a superb exposition with proofs, explanations, history, from D Choimet and H Queffelec:
Twelve Landmarks of Twentieth-Century Analysis
answered 37 mins ago
community wiki
Conrad
add a comment |
add a comment |
$begingroup$
For a casual book on cryptography and the mathematics behind it, I'll recommend Simon Singh's 'The Code Book'. The concept of modular mathematics and public key cryptography are explained beautifully.
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add a comment |
$begingroup$
For a casual book on cryptography and the mathematics behind it, I'll recommend Simon Singh's 'The Code Book'. The concept of modular mathematics and public key cryptography are explained beautifully.
$endgroup$
add a comment |
$begingroup$
For a casual book on cryptography and the mathematics behind it, I'll recommend Simon Singh's 'The Code Book'. The concept of modular mathematics and public key cryptography are explained beautifully.
$endgroup$
For a casual book on cryptography and the mathematics behind it, I'll recommend Simon Singh's 'The Code Book'. The concept of modular mathematics and public key cryptography are explained beautifully.
answered 25 mins ago
community wiki
Jay
add a comment |
add a comment |
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3
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Dieudonne has a few maths history books on algebraic geometry and algebraic geometry, which explain the context in which these fields developed. The Grothendieck-Serre correspondence contains an exchange of letters of who might be the most influential postwar mathematicians. Villani has his book "the birth of a theorem" or something like that.
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– Mere Scribe
9 hours ago
1
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This is not history of mathematics, and I don't know if the material can be considered "advanced" in any sense but looks fun: bookstore.ams.org/mbk-46
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– Qfwfq
9 hours ago
1
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I really liked Love & Math by Edward Frenkel.
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– Fred Rohrer
9 hours ago
1
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I really enjoyed History of Topology by I.M. James. It's a very casual read, but walks you through a lot of "advanced" mathematics.
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– yousuf soliman
7 hours ago
1
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Not a book, but the ICM surveys (impa.br/icm2018) are often great for getting a very basic idea of what's going on in various fields outside of one's own.
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– Sam Hopkins
3 hours ago