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Book recommendation, getting back into mathematics
what textbook would be good as a precursor to discrete mathematics?Book Reference for Calculus and Linear Algebra :: EngineerIn what way is combinatorial game theory connected to the rest of mathematics?Discrete mathematics for someone from a non-mathematical backgroundAre mathematics competitions important?Graduate level elementary logic booksGuidance regarding research in Mathematical PhysicsTextbook Recommendation for Brushing up on Elementary Freshman/Sophomore Level MathematicsPassion for Mathematics versus its role in Computer ScienceLooking for a rigorous analysis book
$begingroup$
First some background, I am originally a computer scientist, got a bachelor at university, started working. I had always had a passion for mathematics and I was relatively good at it throughout my courses. I had done things like linear algebra, a bit past inverses of 3x3 matrices, multivariable calculus , a bit of analysis. I have the mathematical maturity to work through proof heavy texts and I prefer books to learn, I also don't mind spending a long time on very large books either (say 1000 pages+) or a lot and lot of questions.
It has however been a very long while, currently I would say I have regressed a bit worse than the average high school student in mathematics. I can say things like I sort of remember how to do inverses of 3x3 matrices and I could do them. I am however far too rusty and want to brush up my mathematics. It has gotten to the point where matrices , trigonometry and standard angle chasing are all the same difficulty to me simply because my foundation is crumbling.
I had a look back at some real analysis and I seem to be able to make progress until I hit any spots where my foundation is weak at which point it slows me down but doesn't stop nor patch any points in my foundation. I believe it is better to restart my mathematical path from the ground up to tackle any weaknesses before I continue with more abstract content.
Is there any book or set of books that suit my need?
I also have access to a very large library so I believe I should be able to get my hands on any book, I can't seem to follow video lectures as well as books though.
I am particularly interested in:
- Combinatorics
- Statistics
- Algebraic Geometry
- Topology
- Logic
- Analysis
Any help is greatly appreciated.
soft-question book-recommendation
edited Mar 13 at 19:05
Clayton
19.5k33287
asked Mar 13 at 19:01
stevens benjaminstevens benjamin
62
New contributor
stevens benjamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
First some background, I am originally a computer scientist, got a bachelor at university, started working. I had always had a passion for mathematics and I was relatively good at it throughout my courses. I had done things like linear algebra, a bit past inverses of 3x3 matrices, multivariable calculus , a bit of analysis. I have the mathematical maturity to work through proof heavy texts and I prefer books to learn, I also don't mind spending a long time on very large books either (say 1000 pages+) or a lot and lot of questions.
It has however been a very long while, currently I would say I have regressed a bit worse than the average high school student in mathematics. I can say things like I sort of remember how to do inverses of 3x3 matrices and I could do them. I am however far too rusty and want to brush up my mathematics. It has gotten to the point where matrices , trigonometry and standard angle chasing are all the same difficulty to me simply because my foundation is crumbling.
I had a look back at some real analysis and I seem to be able to make progress until I hit any spots where my foundation is weak at which point it slows me down but doesn't stop nor patch any points in my foundation. I believe it is better to restart my mathematical path from the ground up to tackle any weaknesses before I continue with more abstract content.
Is there any book or set of books that suit my need?
I also have access to a very large library so I believe I should be able to get my hands on any book, I can't seem to follow video lectures as well as books though.
I am particularly interested in:
- Combinatorics
- Statistics
- Algebraic Geometry
- Topology
- Logic
- Analysis
Any help is greatly appreciated.
soft-question book-recommendation
edited Mar 13 at 19:05
Clayton
19.5k33287
asked Mar 13 at 19:01
stevens benjaminstevens benjamin
62
New contributor
stevens benjamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Just to try to clarify, are you asking for beginning books as well as advanced texts (the beginning books to become reacquainted with foundational material)? Often times, advanced texts include appendices with some basic information, but these "chapters" have a tendency to be pretty terse and not enlightening, expecting you to already know the material.
$endgroup$
– Clayton
Mar 13 at 19:04
$begingroup$
For logic/set theory I can recommend Set theory by Thomas Jech. For topology there is Algebraic Topology by Allen Hatcher. I am not sure if this is what you may be looking for in combinatorics, but there is Combinatorial Optimization by Jens Vygen
$endgroup$
– Pink Panther
Mar 13 at 19:21
$begingroup$
@Clayton Yes I am, the appendices do juggle my memory, but they often do not return my flexibility. As such there is more of an emphasis on beginning books rather than the advanced for me. I do plan to visit them afterwards or to begin with if it would be more efficient to do so for certain fields or books as certain books explain things from the ground up.
$endgroup$
– stevens benjamin
Mar 14 at 0:28
$begingroup$
@stevensbenjamin: Some good places to learn some things as well as get practice with proofs is either an easy linear algebra textbook (I don't have much experience, but the university I work at uses Linear Algebra by Friedberg et al.) or elementary number theory or abstract algebra texts (a couple of good ones: William LeVeque or George Andrews each have an introductory book on number theory, and Charles Pinter has an introductory textbook on abstract algebra...the latter includes a touch of elementary number theory, too).
$endgroup$
– Clayton
Mar 14 at 3:43
add a comment |
$begingroup$
First some background, I am originally a computer scientist, got a bachelor at university, started working. I had always had a passion for mathematics and I was relatively good at it throughout my courses. I had done things like linear algebra, a bit past inverses of 3x3 matrices, multivariable calculus , a bit of analysis. I have the mathematical maturity to work through proof heavy texts and I prefer books to learn, I also don't mind spending a long time on very large books either (say 1000 pages+) or a lot and lot of questions.
It has however been a very long while, currently I would say I have regressed a bit worse than the average high school student in mathematics. I can say things like I sort of remember how to do inverses of 3x3 matrices and I could do them. I am however far too rusty and want to brush up my mathematics. It has gotten to the point where matrices , trigonometry and standard angle chasing are all the same difficulty to me simply because my foundation is crumbling.
I had a look back at some real analysis and I seem to be able to make progress until I hit any spots where my foundation is weak at which point it slows me down but doesn't stop nor patch any points in my foundation. I believe it is better to restart my mathematical path from the ground up to tackle any weaknesses before I continue with more abstract content.
Is there any book or set of books that suit my need?
I also have access to a very large library so I believe I should be able to get my hands on any book, I can't seem to follow video lectures as well as books though.
I am particularly interested in:
- Combinatorics
- Statistics
- Algebraic Geometry
- Topology
- Logic
- Analysis
Any help is greatly appreciated.
soft-question book-recommendation
edited Mar 13 at 19:05
Clayton
19.5k33287
asked Mar 13 at 19:01
stevens benjaminstevens benjamin
62
New contributor
stevens benjamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
First some background, I am originally a computer scientist, got a bachelor at university, started working. I had always had a passion for mathematics and I was relatively good at it throughout my courses. I had done things like linear algebra, a bit past inverses of 3x3 matrices, multivariable calculus , a bit of analysis. I have the mathematical maturity to work through proof heavy texts and I prefer books to learn, I also don't mind spending a long time on very large books either (say 1000 pages+) or a lot and lot of questions.
It has however been a very long while, currently I would say I have regressed a bit worse than the average high school student in mathematics. I can say things like I sort of remember how to do inverses of 3x3 matrices and I could do them. I am however far too rusty and want to brush up my mathematics. It has gotten to the point where matrices , trigonometry and standard angle chasing are all the same difficulty to me simply because my foundation is crumbling.
I had a look back at some real analysis and I seem to be able to make progress until I hit any spots where my foundation is weak at which point it slows me down but doesn't stop nor patch any points in my foundation. I believe it is better to restart my mathematical path from the ground up to tackle any weaknesses before I continue with more abstract content.
Is there any book or set of books that suit my need?
I also have access to a very large library so I believe I should be able to get my hands on any book, I can't seem to follow video lectures as well as books though.
I am particularly interested in:
- Combinatorics
- Statistics
- Algebraic Geometry
- Topology
- Logic
- Analysis
Any help is greatly appreciated.
soft-question book-recommendation
soft-question book-recommendation
edited Mar 13 at 19:05
Clayton
19.5k33287
asked Mar 13 at 19:01
stevens benjaminstevens benjamin
62
New contributor
stevens benjamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Mar 13 at 19:05
Clayton
19.5k33287
asked Mar 13 at 19:01
stevens benjaminstevens benjamin
62
New contributor
stevens benjamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Mar 13 at 19:05
Clayton
19.5k33287
edited Mar 13 at 19:05
Clayton
19.5k33287
edited Mar 13 at 19:05
Clayton
19.5k33287
19.5k33287
asked Mar 13 at 19:01
stevens benjaminstevens benjamin
62
New contributor
stevens benjamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 13 at 19:01
stevens benjaminstevens benjamin
62
asked Mar 13 at 19:01
stevens benjaminstevens benjamin
62
62
New contributor
stevens benjamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
stevens benjamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
stevens benjamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
Just to try to clarify, are you asking for beginning books as well as advanced texts (the beginning books to become reacquainted with foundational material)? Often times, advanced texts include appendices with some basic information, but these "chapters" have a tendency to be pretty terse and not enlightening, expecting you to already know the material.
$endgroup$
– Clayton
Mar 13 at 19:04
$begingroup$
For logic/set theory I can recommend Set theory by Thomas Jech. For topology there is Algebraic Topology by Allen Hatcher. I am not sure if this is what you may be looking for in combinatorics, but there is Combinatorial Optimization by Jens Vygen
$endgroup$
– Pink Panther
Mar 13 at 19:21
$begingroup$
@Clayton Yes I am, the appendices do juggle my memory, but they often do not return my flexibility. As such there is more of an emphasis on beginning books rather than the advanced for me. I do plan to visit them afterwards or to begin with if it would be more efficient to do so for certain fields or books as certain books explain things from the ground up.
$endgroup$
– stevens benjamin
Mar 14 at 0:28
$begingroup$
@stevensbenjamin: Some good places to learn some things as well as get practice with proofs is either an easy linear algebra textbook (I don't have much experience, but the university I work at uses Linear Algebra by Friedberg et al.) or elementary number theory or abstract algebra texts (a couple of good ones: William LeVeque or George Andrews each have an introductory book on number theory, and Charles Pinter has an introductory textbook on abstract algebra...the latter includes a touch of elementary number theory, too).
$endgroup$
– Clayton
Mar 14 at 3:43
add a comment |
1
$begingroup$
Just to try to clarify, are you asking for beginning books as well as advanced texts (the beginning books to become reacquainted with foundational material)? Often times, advanced texts include appendices with some basic information, but these "chapters" have a tendency to be pretty terse and not enlightening, expecting you to already know the material.
$endgroup$
– Clayton
Mar 13 at 19:04
$begingroup$
For logic/set theory I can recommend Set theory by Thomas Jech. For topology there is Algebraic Topology by Allen Hatcher. I am not sure if this is what you may be looking for in combinatorics, but there is Combinatorial Optimization by Jens Vygen
$endgroup$
– Pink Panther
Mar 13 at 19:21
$begingroup$
@Clayton Yes I am, the appendices do juggle my memory, but they often do not return my flexibility. As such there is more of an emphasis on beginning books rather than the advanced for me. I do plan to visit them afterwards or to begin with if it would be more efficient to do so for certain fields or books as certain books explain things from the ground up.
$endgroup$
– stevens benjamin
Mar 14 at 0:28
$begingroup$
@stevensbenjamin: Some good places to learn some things as well as get practice with proofs is either an easy linear algebra textbook (I don't have much experience, but the university I work at uses Linear Algebra by Friedberg et al.) or elementary number theory or abstract algebra texts (a couple of good ones: William LeVeque or George Andrews each have an introductory book on number theory, and Charles Pinter has an introductory textbook on abstract algebra...the latter includes a touch of elementary number theory, too).
$endgroup$
– Clayton
Mar 14 at 3:43
1
1
$begingroup$
Just to try to clarify, are you asking for beginning books as well as advanced texts (the beginning books to become reacquainted with foundational material)? Often times, advanced texts include appendices with some basic information, but these "chapters" have a tendency to be pretty terse and not enlightening, expecting you to already know the material.
$endgroup$
– Clayton
Mar 13 at 19:04
$begingroup$
Just to try to clarify, are you asking for beginning books as well as advanced texts (the beginning books to become reacquainted with foundational material)? Often times, advanced texts include appendices with some basic information, but these "chapters" have a tendency to be pretty terse and not enlightening, expecting you to already know the material.
$endgroup$
– Clayton
Mar 13 at 19:04
$begingroup$
For logic/set theory I can recommend Set theory by Thomas Jech. For topology there is Algebraic Topology by Allen Hatcher. I am not sure if this is what you may be looking for in combinatorics, but there is Combinatorial Optimization by Jens Vygen
$endgroup$
– Pink Panther
Mar 13 at 19:21
$begingroup$
For logic/set theory I can recommend Set theory by Thomas Jech. For topology there is Algebraic Topology by Allen Hatcher. I am not sure if this is what you may be looking for in combinatorics, but there is Combinatorial Optimization by Jens Vygen
$endgroup$
– Pink Panther
Mar 13 at 19:21
$begingroup$
@Clayton Yes I am, the appendices do juggle my memory, but they often do not return my flexibility. As such there is more of an emphasis on beginning books rather than the advanced for me. I do plan to visit them afterwards or to begin with if it would be more efficient to do so for certain fields or books as certain books explain things from the ground up.
$endgroup$
– stevens benjamin
Mar 14 at 0:28
$begingroup$
@Clayton Yes I am, the appendices do juggle my memory, but they often do not return my flexibility. As such there is more of an emphasis on beginning books rather than the advanced for me. I do plan to visit them afterwards or to begin with if it would be more efficient to do so for certain fields or books as certain books explain things from the ground up.
$endgroup$
– stevens benjamin
Mar 14 at 0:28
$begingroup$
@stevensbenjamin: Some good places to learn some things as well as get practice with proofs is either an easy linear algebra textbook (I don't have much experience, but the university I work at uses Linear Algebra by Friedberg et al.) or elementary number theory or abstract algebra texts (a couple of good ones: William LeVeque or George Andrews each have an introductory book on number theory, and Charles Pinter has an introductory textbook on abstract algebra...the latter includes a touch of elementary number theory, too).
$endgroup$
– Clayton
Mar 14 at 3:43
$begingroup$
@stevensbenjamin: Some good places to learn some things as well as get practice with proofs is either an easy linear algebra textbook (I don't have much experience, but the university I work at uses Linear Algebra by Friedberg et al.) or elementary number theory or abstract algebra texts (a couple of good ones: William LeVeque or George Andrews each have an introductory book on number theory, and Charles Pinter has an introductory textbook on abstract algebra...the latter includes a touch of elementary number theory, too).
$endgroup$
– Clayton
Mar 14 at 3:43
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Not a complete answer but too long for a comment
For topology, a nice beginner textbook is Munkres's text Topology while Willard's textbook General Topology is a bit deeper (I prefer the second one, but if I hadn't already taken a class with topology, I think the first one is easier to self-teach from). If you want to delve beyond general topology and touch on algebraic topology, Hatcher has a nice textbook that is freely available online.
For analysis, a couple of beginner-type textbooks are Wade's text An Introduction to Real Analysis and, a bit more difficult but still at the beginner level, Rudin's Principles of Mathematical Analysis. I think some top-notch recommendations for analysis texts are Rudin's Real and Complex Analysis as well as Ahlfors's Complex Analysis. A comprehensive overview of complex analysis can be found in Markushevich's text Theory of Functions of a Complex Variable.
$endgroup$
add a comment |
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$begingroup$
Not a complete answer but too long for a comment
For topology, a nice beginner textbook is Munkres's text Topology while Willard's textbook General Topology is a bit deeper (I prefer the second one, but if I hadn't already taken a class with topology, I think the first one is easier to self-teach from). If you want to delve beyond general topology and touch on algebraic topology, Hatcher has a nice textbook that is freely available online.
For analysis, a couple of beginner-type textbooks are Wade's text An Introduction to Real Analysis and, a bit more difficult but still at the beginner level, Rudin's Principles of Mathematical Analysis. I think some top-notch recommendations for analysis texts are Rudin's Real and Complex Analysis as well as Ahlfors's Complex Analysis. A comprehensive overview of complex analysis can be found in Markushevich's text Theory of Functions of a Complex Variable.
$endgroup$
add a comment |
$begingroup$
Not a complete answer but too long for a comment
For topology, a nice beginner textbook is Munkres's text Topology while Willard's textbook General Topology is a bit deeper (I prefer the second one, but if I hadn't already taken a class with topology, I think the first one is easier to self-teach from). If you want to delve beyond general topology and touch on algebraic topology, Hatcher has a nice textbook that is freely available online.
For analysis, a couple of beginner-type textbooks are Wade's text An Introduction to Real Analysis and, a bit more difficult but still at the beginner level, Rudin's Principles of Mathematical Analysis. I think some top-notch recommendations for analysis texts are Rudin's Real and Complex Analysis as well as Ahlfors's Complex Analysis. A comprehensive overview of complex analysis can be found in Markushevich's text Theory of Functions of a Complex Variable.
$endgroup$
add a comment |
$begingroup$
Not a complete answer but too long for a comment
For topology, a nice beginner textbook is Munkres's text Topology while Willard's textbook General Topology is a bit deeper (I prefer the second one, but if I hadn't already taken a class with topology, I think the first one is easier to self-teach from). If you want to delve beyond general topology and touch on algebraic topology, Hatcher has a nice textbook that is freely available online.
For analysis, a couple of beginner-type textbooks are Wade's text An Introduction to Real Analysis and, a bit more difficult but still at the beginner level, Rudin's Principles of Mathematical Analysis. I think some top-notch recommendations for analysis texts are Rudin's Real and Complex Analysis as well as Ahlfors's Complex Analysis. A comprehensive overview of complex analysis can be found in Markushevich's text Theory of Functions of a Complex Variable.
$endgroup$
Not a complete answer but too long for a comment
For topology, a nice beginner textbook is Munkres's text Topology while Willard's textbook General Topology is a bit deeper (I prefer the second one, but if I hadn't already taken a class with topology, I think the first one is easier to self-teach from). If you want to delve beyond general topology and touch on algebraic topology, Hatcher has a nice textbook that is freely available online.
For analysis, a couple of beginner-type textbooks are Wade's text An Introduction to Real Analysis and, a bit more difficult but still at the beginner level, Rudin's Principles of Mathematical Analysis. I think some top-notch recommendations for analysis texts are Rudin's Real and Complex Analysis as well as Ahlfors's Complex Analysis. A comprehensive overview of complex analysis can be found in Markushevich's text Theory of Functions of a Complex Variable.
edited Mar 13 at 19:18
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stevens benjamin is a new contributor. Be nice, and check out our Code of Conduct.
stevens benjamin is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
Just to try to clarify, are you asking for beginning books as well as advanced texts (the beginning books to become reacquainted with foundational material)? Often times, advanced texts include appendices with some basic information, but these "chapters" have a tendency to be pretty terse and not enlightening, expecting you to already know the material.
$endgroup$
– Clayton
Mar 13 at 19:04
$begingroup$
For logic/set theory I can recommend Set theory by Thomas Jech. For topology there is Algebraic Topology by Allen Hatcher. I am not sure if this is what you may be looking for in combinatorics, but there is Combinatorial Optimization by Jens Vygen
$endgroup$
– Pink Panther
Mar 13 at 19:21
$begingroup$
@Clayton Yes I am, the appendices do juggle my memory, but they often do not return my flexibility. As such there is more of an emphasis on beginning books rather than the advanced for me. I do plan to visit them afterwards or to begin with if it would be more efficient to do so for certain fields or books as certain books explain things from the ground up.
$endgroup$
– stevens benjamin
Mar 14 at 0:28
$begingroup$
@stevensbenjamin: Some good places to learn some things as well as get practice with proofs is either an easy linear algebra textbook (I don't have much experience, but the university I work at uses Linear Algebra by Friedberg et al.) or elementary number theory or abstract algebra texts (a couple of good ones: William LeVeque or George Andrews each have an introductory book on number theory, and Charles Pinter has an introductory textbook on abstract algebra...the latter includes a touch of elementary number theory, too).
$endgroup$
– Clayton
Mar 14 at 3:43