
Ask HN: Math books like SICP? - nextos
I&#x27;d like to start learning undergrad math at a rigorous level.<p>As a CS grad I already covered certain topics like abstract algebra at a respectable level. But I&#x27;m lacking consistent and broad knowledge throughout all areas.<p>I&#x27;m looking for math books covering undergrad topics like SICP, which Peter Norvig described as &quot;[...] a way of synthesizing what you already know, and building a rich framework onto which you can add new learning over a career&quot; [1].<p>[1] http:&#x2F;&#x2F;www.amazon.com&#x2F;review&#x2F;R403HR4VL71K8
======
oskarth
Not the same type of book, but you could do a lot worse than reading through
_Mathematics: Its Content, Methods and Meaning_ , by M. A. Lavrent’ev, A. D.
Aleksandrov, A. N. Kolmogorov. It's an amazing book which gives a mathematical
(but not rigorous in the sense of proofs etc.) overview of most of
mathematics.

[http://www.amazon.com/Mathematics-Content-Methods-Meaning-
Do...](http://www.amazon.com/Mathematics-Content-Methods-Meaning-
Dover/dp/0486409163/)

~~~
hf
Absolutely astounding: I have been looking for this book ever since I pored
over it in the Wolfson Reading Room in Manchester Central Library 5 years ago.
I didn't take down the authors' names, though, referring to it as "that yellow
mathematics book" then and ever since.

I credit that book with much if not all my mathematical insight.

Thank you.

(Just seeing that cover leaves me all tear-eyed, reminiscing over that
wonderfully irresponsible time.)

~~~
auvrw
> "that yellow mathematics book"

replace "that" with "those" (
[http://en.wikipedia.org/wiki/Graduate_Texts_in_Mathematics](http://en.wikipedia.org/wiki/Graduate_Texts_in_Mathematics)
).

the dover books are also a good series, and pretty much anything by Artin is
good. i also looked at the Halmos book a couple of people have mentioned.

perhaps one thing to be aware of, though, is that you're not always going to
learn things in the linear way they're layed out on the page. moreover, it
might be helpful to have more than one book for any given subject. Lang's
Algebra, for example, is a really good reference, but a tome if you read it
like a text. so you might pick up something small and subject-oriented with a
lot of exercises like Artin's Galois Theory or Atiyah's Commutative Algebra,
and supplement it with a reference like Dummit and Foote or Lang's texts on
Algebra as a whole.

oh, right: whatever book you choose, _do the exercises_.

~~~
pervycreeper
But that's not a Springer book, it appears to be published by Dover, and the
covers look totally different. The GTM series is also highly variable in
quality.

~~~
auvrw
perhaps the GTM series has some bad titles; i haven't read them all. but it
has some good titles, and from the description original poster's background,
it's probably as far as the person wants to stretch right now. sure, the
cambridge advanced math series might be more "quality," but those also tend to
be both very focused (in terms of specificity of the topic) and very dense (in
terms of delivering a lot of results with almost zero fluff).

------
j2kun
Sheldon Axler's "Linear Algebra Done Right" has my highest recommendation if
you want expertise in linear algebra.

As a followup, Paolo Aluffi's "Algebra: Chapter Zero" is the best synthesizing
text for abstract algebra for a beginning graduate student. The thing that
makes it so amazing is the writing style: it introduces and demystifies
category theory, and then discusses groups, rings, modules, linear algebra,
fields, r-modules, and advanced topics (toward the end) with the unifying
theme of how they work and relate as categories. It is very much a book that
focuses on the why over the what and how. And there are many many many juicy
exercises.

I would recommend against Spivak's Calculus on manifolds. It's too dense and
too focused on advanced topics (unless you're an ivy league undergrad, you
don't learn cohomology). That being said I don't have an analysis reference
that fits your request.

As a CS person I can continue with book recommendations related to computing-
related topics in math (computational algebraic geometry comes to mind). Let
me know if you're interested.

~~~
nextos
Thanks. Axler's LADR is indeed fantastic, I have already worked through 1/2 of
it. I'm really happy to see my opinion seconded. It's really short and
precise. Some people seem to prefer Halmos' Finite Dimensional Vector Spaces,
but I found the presentation less didactic. Perhaps it's also more of an upper
division text, and I'm not there yet.

I was looking for a real analysis companion, perhaps baby Rudin. I was also
wondering whether it'd make sense to proceed directly to real analysis, or to
step down a bit and read something like Spivak's Calculus.

I'd also like to hear about recommendations at undergrad level in the fields
of logic and set theory, geometry, combinatorics, and probability theory.
Those would complete my basic math curriculum.

~~~
jjoonathan
I third the recommendation on Axler's LADR.

I'd actually like to hear about alternatives to Rudin. My undergrad analysis
class used it, but it's lack of diagrams was particularly bothersome. I'd
spend an hour digesting a rat's nest of a paragraph only to discover that the
underlying concept was simple enough that even a rough sketch ought to be able
to get the gist of it across in seconds.

~~~
caraboga
Wade's an easier book that has more undergraduate aids.
[http://www.amazon.com/Introduction-Analysis-Edition-
William-...](http://www.amazon.com/Introduction-Analysis-Edition-William-
Wade/dp/0132296381)

I also like Strang for Linear Algebra for undergrads. Beyond that it's Hoffman
and Kunze.

------
cottonseed
You might be interested in this math.SE question I asked:

[https://math.stackexchange.com/questions/62190/mathematical-...](https://math.stackexchange.com/questions/62190/mathematical-
equivalent-of-feynmans-lectures-on-physics)

(comparing to Feynman's Lectures on Physics rather than SICP.)

However, I agree with zodiac: Math is a much broader field and I think very
few living people have the kind knowledge you're talking about: consistent and
broad knowledge in all areas.

I have the same background as you and I started doing exactly this about 8
years ago. I'm just finishing my PhD in math. I'll give you some advice.
First, studying math for its own sake by yourself is extremely hard. That's
one reason I ended up back in academia. If you can't go back to school, still
find some kind of community. Second, rather than studying generally, try to
identify a goal to work towards. What are you trying to understand or figure
out? Third, try to model your plan on a rigorous undergrad program, e.g., MIT.
Then, in each main undergrad area (algebra, analysis, topology, geometry,
etc.) try to find the "SICP" and study that. For general book recommendations,
I like Fowler's A Mathematics Autodidact's Aid:

[http://www.ams.org/notices/200510/comm-
fowler.pdf](http://www.ams.org/notices/200510/comm-fowler.pdf)

~~~
krick
> [http://www.ams.org/notices/200510/comm-
> fowler.pdf](http://www.ams.org/notices/200510/comm-fowler.pdf)

That's great one! Thank you for pointing this out very much.

------
karamazov
I'm a big fan of SICP. I'd describe it as "hard-core": requiring hard work,
but extremely rewarding for the people who take the time and effort to go
through it.

I'd recommend the following three books to similarly cover the three main
areas of higher mathematics (analysis, algebra, and topology):

1\. Principles of Mathematical Analysis by Rudin
([http://www.amazon.com/Principles-Mathematical-Analysis-
Inter...](http://www.amazon.com/Principles-Mathematical-Analysis-
International-Mathematics/dp/007054235X))

2\. Algebra by Artin ([http://www.amazon.com/Algebra-2nd-Featured-Titles-
Abstract/d...](http://www.amazon.com/Algebra-2nd-Featured-Titles-
Abstract/dp/0132413779))

3\. Topology by Munkres ([http://www.amazon.com/Topology-2nd-James-
Munkres/dp/01318162...](http://www.amazon.com/Topology-2nd-James-
Munkres/dp/0131816292))

Working through all three (including the exercises!) will give you a solid
understanding of the basis of modern mathematics. If you don't have experience
with proofwriting, you might find them difficult at first - the activity is
very different from performing calculations or solving equations. It's also
best to have someone trained in mathematics talk to you about the proofs,
until you develop a feel for the needed level of logical rigor.

Rudin, in particular, leaves a lot of work to the reader; going through that
book is the most intellectually difficult work I've ever done. If you find it
hard-going (which is completely natural), you might want to try Artin first,
especially since you have some background in algebra.

(Incidentally, these are the three books used to teach analysis, algebra, and
topology to MIT mathematics majors. You can look up the assignments and exams
for the three courses - 18.100B, 18.701, and 18.901 - for a good list of
exercises to work through.)

~~~
radmuzom
Great list. Another addition to the list would be

4\. Topics in Algebra by I.N.Herstein.

It has a slightly better (and tougher) set of problems than what you would
find in the book by Artin.

------
htns
The Princeton Companion to Mathematics [1] is good if you want to gawk at the
breadth and depth of the field. For actual education I would just suggest
looking at a math department's syllabus, e.g. at
[http://ocw.mit.edu/](http://ocw.mit.edu/). As a CS grad you should start with
analysis, as that's probably your most looming dark spot.

My warning as a math student is that a lot of book recommendations are just a
tad bit elitist. Don't stick with a single book too long if it isn't cutting
it for self-study. Exercises are good.

[1]
[http://press.princeton.edu/titles/8350.html](http://press.princeton.edu/titles/8350.html)

~~~
LanceH
The Princeton Companion should come with a warning label.

------
gms
It's difficult to find what you are looking for, since maths is a much older
field. However, Spivak's 'Calculus' is pretty close:
[http://www.amazon.com/gp/aw/d/0914098918](http://www.amazon.com/gp/aw/d/0914098918).

~~~
cabacon
I clicked on this topic in order to make this suggestion. To expand on it a
little bit, I was a math major and read Spivak's 'Calculus' after I had
already taken real analysis. I found it delightful - it really approaches the
topics from first principles and unlike many calculus textbooks actually goes
through the effort of presenting proofs of the theorems. Highly recommended.

As some recreational reading, less suiting the original request, I very much
enjoyed David Foster Wallace's 'Everything and More: A Compact History of
Infinity' ([http://www.amazon.com/Everything-More-Compact-History-
Infini...](http://www.amazon.com/Everything-More-Compact-History-
Infinity/dp/0393339289/)). DFW is not for everyone, but I enjoyed it a lot.
Maybe just check it out of the library first to see if it's for you.

~~~
lambdaphage
I appreciated DFW's book for even attempting to do a popular treatment of what
we would now call the history of real analysis. But there were some serious
technical problems with it: [http://www.ams.org/notices/200406/rev-
harris.pdf](http://www.ams.org/notices/200406/rev-harris.pdf)

------
Grothendieck
SICP doesn't really cover very much in the grand scheme of CS, so "like SICP"
might mean ...

... something covering "how to do math". This might be an introductory real
analysis or linear algebra book, or (alas, I haven't read much in this area)
you could do no wrong looking for books on problem solving, contests, and
inequalities, say by Polya or Andreescu.

... a higher-level view of day-to-day mathematical practice. There probably
isn't one book for this, but I'd recommend Loomis and Sternberg's _Advanced
Calculus_ as a summation of linear algebra and calculus on manifolds; you'd
also need to read on complex and functional analysis, algebra (Lang and the
unofficial companion volume?), topology ...

... a broad but shallow introduction to several fields and applications
unified but a common underlying approach (abstraction and programming language
design). I'd recommend Geroch's _Mathematical physics_ , which, as the name
implies, studies algebra, algebraic topology, and functional analysis through
the common lens of category theory.

... a somewhat quirky book on foundations? You could look for a book on naive
or axiomatic set theory, categories, or type theory.

------
mahmud
Run, don't walk, and get "An Introduction to Mathematical Reasoning"by Peter
Eccles. That will open your eyes to mathematics, as done by mathematicians.

After that, anything by Serge Lang. He is a first-rate mathematician and a
fine educator. A master of mathematical exposition, a rare talent.

I started with two books: "Principles of Mathematical Analysis" by Walter
Rudin, and "Abstract Algebra" by Israel Herstein. Keyword is "started". Nearly
every paragraph of either book sent me to a goose-chase of research and
reading up on supporting materials. Safe to say that by the time I was nearly
done with either, I have acquired about 50 other math books and had about zero
social life ;-)

Good news is that good math books are _cheap_ , compared to anything
computing. You can find classics for $1-$5 in most yard sales and 2nd hand
bookstores. The trick is to buy _thin_ math books; the giant, multi-color text
books they use in schools are highly confusing, at least to me. It's 200 pages
of math stretched to 1200, with a similar jump in price.

Mathematics is both style and substance. Once you get the hang of the basic
language, the succinct delivery style, the proofs and generalizations, how
notation is introduced and then elided when it becomes too apparent .. all
these will add up to help you navigate more "advanced" texts. You will come to
recognize what is a well-posed mathematical problem, and what is not, even if
you don't understand the domain itself.

Finally, if you have the option to study this formally at an institution, do
it. The 2nd best option is to find a friend that shares this interest and
discuss things. I didn't study it formally, but I was a barista at a coffee
shop with plenty of mathphile customers. I had a lot of 1:1 instruction for
highly qualified people on my 10 minute breaks :-)

------
lquist
The Chicago undergraduate mathematics bibliography is a fantastic list:
[http://www.ocf.berkeley.edu/~abhishek/chicmath.htm](http://www.ocf.berkeley.edu/~abhishek/chicmath.htm).

~~~
j2kun
What a fantastically long list! But it appears to be a bit dated. For example,
the Algebraic Topology section doesn't have either of Hatcher or Munkres,
which are the standard graduate texts nowadays.

Update: yeah this list was last updated in 2000.

------
zodiac
Math is a much, much broader field than the part of Computer Science than SICP
covers, so it's really hard to search for "consistent and broad knowledge
throughout all areas". Do you really need to learn analytic number theory?
category theory? axiomatic set theory? tensor calculus?

My suggestion would be to narrow it down to a specific field you're interested
in like abstract algebra and ask for suggestions about that field. Even
narrowed down the field might be too big - a basic introduction to abstract
algebra would probably contain the same amount of information as SICP.

CS people tend to find discrete math and linear algebra most useful in their
work, but maybe you want to learn something just for the sake of it and not
for work.

~~~
nextos
I was planning to structure my learning around linear algebra and real
analysis, sort of like Harvard's Math 55 does.

Apart from that I wanted to expand on basic set theory, geometry,
combinatorics and probability theory to have a well-rounded basic education.

My ultimate goal is to be able to digest advanced probability and statistics
books.

~~~
pmiller2
Set theory: You should definitely look at _Naive Set Theory_ by Halmos.
Despite the name, it's totally rigorous development of ZF set theory with
discussion on the meaning and equivalent statements of AC.

~~~
nextos
What about Lawvere's _Conceptual Mathematics_ or _Sets for Mathematics_?

------
cage433
Also by Sussman - well worth looking into

[http://mitpress.mit.edu/sites/default/files/titles/content/s...](http://mitpress.mit.edu/sites/default/files/titles/content/sicm/book.html)

~~~
reikonomusha
As I said elsewhere in this thread, this is _not_ like SICP.

------
jvreeland
It's not nearly as easy to work through as SICP is but Principles of
Mathematical Analysis by Walter Rudin (sometimes referred to as little Rudin)
is a great place to start if you're interested in analysis. It's a hard book,
but it's pretty much the standard for undergrad analysis.

~~~
dominotw
Baby Rudin still gives me nightmares.

~~~
jvreeland
Real Analysis by Royden is the source of my nightmares.

~~~
graycat
Royden is breathtakingly gorgeous. But, it can be good to skip some parts.

The main content is just 'measure theory', and that's just freshman calculus
grown up. Why? Because near 1900 it became clear that freshman calculus was
clumsy for some important progress, especially cases of convergence of
functions.

Measure theory? Well, first cut, 'measure' is just a grown up version of
ordinary area. Simple.

Why interested in measure theory? Because want to cook up a new way to do
integration, that is, what freshman calculus dues with the Riemann integral.
Recall, the Riemann integral partitions the X axis and approximates the area
under the curve with tall, thin rectangles. Measure theory partitions the Y
axis: At first glance this seems a little clumsy, but in the usual cases get
the same number for area under a curve and in bizarre cases, that can get from
converging functions, get a nice answer that Riemann integration can't do.

Royden likes Littlewood's three principles, and they are cute. So, spend an
evening on them. Yes, it's possible to use Littlewood's to do the subject, but
there is a better way, also heavily in Royden, roughly called 'monotone class
arguments' \-- which are gorgeous and turn much of the whole book into
something quite simple. So, prove the theorem for indicator functions. Then
extend to simple functions by linearity. Then extend to non-negative
measurable functions by a monotone sequence. Then extend to integrable
functions by linearity. Can knock off much of the book this way, e.g.,
Fubini's theorem which is just interchange of order of integration grown up.
The foundations of this little four step process is Fatou's lemma, the
monotone convergence theorem, and the dominated convergence theorem.

About 2/3rds of the way through Royden is a single chapter that essentially
compresses much of the rest of the book -- I would have to step into my
library to find the chapter.

For the early exercises on upper and lower semi-continuity, they are a bit
much and you likely won't see that topic again. So that exercise can be
skipped.

Royden is elegant beyond belief; if you still have trouble finding the main
themes, then chat for an hour with a good math proof who understand Royden
well.

Then, don't miss the Radon-Nikodym theorem: It can be seen as a grown up
version of the fundamental theorem of freshman calculus but, really, is much,
much better. The role of the Radon-Nikodym theorem in 'modern' (i.e.,
Kolmogorov) probability theory, stochastic processes, Markov processes,
martingales, etc. is astounding.

~~~
zeta8
I'd agree with your assessment of Royden. Another fantastic book on Lebesgue
Integration/Measure theory is Lebesgue Integration in Euclidean Spaces by
Frank Jones. Fantastic textbook.

------
decasteve
If you've already covered Vector Spaces, Groups, and Rings in your studies, I
would suggest checking out Bill Lawvere's "Conceptual Mathematics: A First
Introduction to Categories". i.e. An introduction to category theory through
the category of sets. His "Sets for Mathematics" is also good but it's a more
concise presentation of the topic but a less than gentle introduction than the
former book.

~~~
tel
I was going to recommend this one. Conceptual Mathematics is wonderful in that
it provides a narrative of intuition instead of just the proofs. It's kind of
like seeing How It Is Made for algebra.

~~~
nextos
Do _Conceptual Mathematics_ and _Sets for Mathematics_ cover the same ground?

~~~
tel
I've only read Conceptual Mathematics; sorry for the confusion.

CM covers Category Theory as a general tool for probing and exploring
algebraic concepts beginning as simply as endomorphism and extending all the
way out to how it can be the foundations of a generalization of set theory via
Toposes... all in a cheery and explorative fashion which really illuminates
why the ideas work instead of merely stating them.

I'm not sure what the required background might be, but it's probably pretty
minimal.

------
Jugurtha
Well, I don't know how it goes over there, but here in Algeria, Engineers go
through two common years (after which they chose a specialty in the third
year, and then, in the fourth and fifth year, a specialty of specialty).

All Engineers go through both years, except Computer Science who don't do the
common second year and they directly go to Computer Science.

In these two years, everyone goes through this (maybe it'll give you some
ideas on what you want to add):

I'll only list the "Maths" we take first and second year:

First year: \- Algebra: (a long course, bottom up. From Boole's algebra, to
groups, sigma-algebra, yadda yadda), linear algebra(vector spaces, etc)..

\- Probabilities and Statistics.

\- Analysis: (Taylor series (Lagrange, Laplace, Young, Cauchy, Maclaurin),
integrals, differentiations, different series, convergence/divergence kung
fu), Riemann overall, proofs, etc.. Functions, multivariable, real and
complex, etc.

Second year:

\- Analysis I - Numerical Analysis (Equation systems, Gauss-Seidel, different
algorithms(also calculating their speeds), Newton-Raphson, extrapolation,
interpolation, etc).

\- Analysis II - Integrals(up to 3rd - curves, areas/surfaces(Green) and
volumes (Ostrogradsky)), Differential equations (Wronskian, etc).

This is the minimum (to be able to function in other modules, and some other
modules are needed before you can function in these, so there's sort of
bootstrapping of sort).

And then it depends what you take as specialty (if it's something involving
Signal Processing, for instance, or Control Systems, you also need to do
stuff).

Hope that helps and you can find some things.

PS: None of these are done with computers, so computing stuff with Newton
algorithm and operations on big matrices are all done by hand. It takes a lot
of time.

PPS: We don't have multiple answer questions. There's a question, and you
answer it (and some answers take multiple pages).

Also, most tests are designed in a way that even if you have the answer sheet
right next to you, it still takes you more time to copy the answers than the
time of the exam itself. i.e: Even if you don't think and only "write", the
time-frame is too tight.

~~~
jimmaswell
you have to retake Algebra even if you did it in high school?

~~~
Derander
I'd be surprised if the average high school algebra course covered group
theory :-).

------
agumonkey
Not Math, but Physics/Mechanics, by Sussman again. Title ? SICM hehe

[https://mitpress.mit.edu/sites/default/files/titles/content/...](https://mitpress.mit.edu/sites/default/files/titles/content/sicm/book.html)

~~~
reikonomusha
SICM is not like SICP at all. SICM assumes you're pretty well versed in
classical mechanics and already have an understanding of both Lagrangian and
Hamiltonian mechanics.

Don't be fooled by the title and authors of the book!

~~~
zbinga
Heh. I bought SICM expecting it would be "SICP for physics". I started reading
and felt out of my depth after just a few pages. But it seemed interesting, so
I got a Lagrangian and Hamiltonian mechanics book and started reading that.
That was 6 months ago, I'm about halfway through and I'm really enjoying it!

Learning Lagrangian mechanics when all your life you only ever heard about the
Newtonian approach is a lot like stumbling upon Scheme after years of
programming in C.

I'm looking forward to cracking the cover of SICM once more this summer!

------
stiff
The only book on mathematics actually reassembling SICP I found is "What is
mathematics?" by Richard Courant. I have read it after reading SICP, largely
because I very much liked some of the more mathematical fragments in SICP, and
surprisingly it felt like an actual follow up - it spends significant amount
of time highlighting high level trends in mathematics, like use of abstraction
and generalization, using very concrete examples. Sounds familiar?

------
midas007
Concrete Mathematics by Ronald Graham, Donald Knuth, and Oren Patashnik

[https://en.wikipedia.org/wiki/Concrete_Mathematics](https://en.wikipedia.org/wiki/Concrete_Mathematics)

Also Knuth's TAOCP series are very formal and dense, in a good way.

~~~
mturmon
_Concrete Mathematics_ is a great book, really good content and techniques
about computing things, and a lot of depth and useful history and side
information.

------
zeta8
I'm in a similar position as well - perhaps at just a wee bit higher level (am
learning grad-level math by myself). Below is a list of books that I have
enjoyed. Some might perhaps be at a slightly higher level than you might need
right now though.

1\. Analysis - The Elias Stein, Rami Shakarchi Analysis series, Meassure
Theory by Terrence Tao, Lebesgue Integration on Euclidean Spaces by Frank
Jones, A radical approach to Lebesgue Integration by Bressoud

2\. Algebra - Can't do much better than the classic texts by Herstein & Artin
here. I know Artin doesn't get much love but after a point, you really begin
to appreciate it.

3\. Complex Analysis - is there a better math book than Visual Complex
Analysis by Needham?

4\. Topology - i'm partial to a Dover book on Topology by Theodore Gamelin. I
learnt the basics of point-set topology & homotopy form this book. Great
exercises.

5\. Number Theory - check out the 2 problem books on number theory by Ram
Murty. Melvyn Nathanson's book is quite good as well.

6\. Combinatorics - Combinatorics of Finite Sets by Ian Anderson. Extremal
Combinatorics by Jukna.

7\. Graph Theory - Diestel or Bondy/Murty.

8\. Galois Theory - Rotman is great.

------
krick
I share exactly the same interest. Can anybody suggest some outline for what
topics (more or less) should somebody cover to be on "undergrad-math" level?

Unfortunately I have to hold my own tongue this time, because books I found
useful are mainly in russian and they surely aren't like SICP. And I still
lack the whole understanding of the area anyway.

~~~
okasaki
All the Mathematics You Missed: But Need to Know for Graduate School -
[http://www.amazon.com/All-Mathematics-You-Missed-
Graduate/dp...](http://www.amazon.com/All-Mathematics-You-Missed-
Graduate/dp/0521797071/)

~~~
krick
Words cannot express how grateful I am. This seems to be the very thing I
looked for the long time and missed somehow! Seems not to cover really _All
the Mathematics I Missed_ however (nothing on algebra and number theory for
example, which is admittedly my weak spot), but I'm already thrilled to start
reading.

------
ivan_ah
Recently, I've been reading this mega book that covers a lot of advanced
topics in math by Kolmogorov et al. It is nice because it covers a lot of
topics w/o in a fairly short text --- it is a brick but it covers 2000 years
of knowledge! [http://www.amazon.com/Mathematics-Content-Methods-Meaning-
Do...](http://www.amazon.com/Mathematics-Content-Methods-Meaning-
Dover/dp/0486409163)

For first-year stuff, I would recommend _No bullshit guide to math and
physics_ [1] and the _No bullshit guide to linear algebra_ [2] of which I am
the author.

[1] [http://minireference.com/](http://minireference.com/) [2]
[http://gum.co/noBSLA](http://gum.co/noBSLA)

------
davidjhall
I'm surprised no one has mention Mathematics for the Millions by Lancelot
Hogben. [http://www.amazon.com/Mathematics-Million-Master-Magic-
Numbe...](http://www.amazon.com/Mathematics-Million-Master-Magic-
Numbers/dp/039331071X/ref=sr_1_1?ie=UTF8&qid=1397347351&sr=8-1&keywords=lancelot+math)

He takes the approach of starting right at the beginning of human history when
we first came to look at the stars and seasons and try to understand why they
work, and then builds the math knowledge with each lesson. Excellent book!

------
adem
My recommendation is "One-Variable-Calculus with and introduction to Linear
Algebra" by Tom M. Apostol, followed by "Mathematical Analysis". Both books
form a great combination!

------
ab-irato
There is a recent book by Sussman and Wisdom that goes over Differential
Geometry with a focus on Physics applications.

[http://groups.csail.mit.edu/mac/users/gjs/6946/calculus-
inde...](http://groups.csail.mit.edu/mac/users/gjs/6946/calculus-indexed.pdf)
[http://www.amazon.com/gp/product/0262019345/](http://www.amazon.com/gp/product/0262019345/)

Edit: included Amazon link.

------
biot
This might be along the lines of what you're looking for:
[http://www.amazon.com/Mathematics-Birth-Numbers-Jan-
Gullberg...](http://www.amazon.com/Mathematics-Birth-Numbers-Jan-
Gullberg/dp/039304002X)

    
    
      "This extraordinary work takes the reader on a long and
       fascinating journey--from the dual invention of numbers
       and language, through the major realms of arithmetic,
       algebra, geometry, trigonometry, and calculus, to the
       final destination of differential equations, with
       excursions into mathematical logic, set theory, topology,
       fractals, probability, and assorted other mathematical
       byways. The book is unique among popular books on
       mathematics in combining an engaging, easy-to-read
       history of the subject with a comprehensive mathematical
       survey text."

------
gtani
I dunno about SICP-like, but here's some good book lists

[https://github.com/ystael/chicago-ug-math-
bib](https://github.com/ystael/chicago-ug-math-bib) (updated Univ of Chicago
bibliography

[http://math.ucr.edu/home/baez/books.html](http://math.ucr.edu/home/baez/books.html)

[http://www.maths.cam.ac.uk/undergrad/course/schedules.pdf](http://www.maths.cam.ac.uk/undergrad/course/schedules.pdf)

______________________

and 2 i got from HN and /r/machineLearning

[http://www.reddit.com/r/MachineLearning/comments/1jeawf/mach...](http://www.reddit.com/r/MachineLearning/comments/1jeawf/machine_learning_books/)

[https://github.com/vhf/free-programming-
books/blob/master/fr...](https://github.com/vhf/free-programming-
books/blob/master/free-programming-books.md#machine-learning)

________________________

finally, the "Maths for PHysics" texts

[http://www.scribd.com/doc/156523189/Boas-mathematical-
Method...](http://www.scribd.com/doc/156523189/Boas-mathematical-Methods-in-
the-Physical-Sciences-pdf)

[http://www.goldbart.gatech.edu/PG_MS_MfP.htm](http://www.goldbart.gatech.edu/PG_MS_MfP.htm)

[http://www.scribd.com/doc/91670553/Arfken-Math-
Physics](http://www.scribd.com/doc/91670553/Arfken-Math-Physics)

___________________

(if i had to recommend only one book, it would be the Boas, or maybe Princeton
Companion:
[http://press.princeton.edu/titles/8350.html](http://press.princeton.edu/titles/8350.html)

------
ced
David Mackay's Information Theory, Inference and Learning algorithms doesn't
cover everything, but it ties up a lot of important topics.

[http://www.inference.phy.cam.ac.uk/mackay/itila/](http://www.inference.phy.cam.ac.uk/mackay/itila/)

------
zbinga
It's not at all like SICP (I've never met a math book that was similar), but
it's a wonderful introduction and I don't see it mentioned in this thread yet:
Needham's "Visual Complex Analysis".

------
dominotw
Spivak's Calculus is like SICP.

------
bananas
Jan Gullberg wrote an excellent book:

Mathematics: from the Birth of Numbers.

It's mainly pure math but is a great foundation. I mean really better than
anything else I've read.

------
fsk
[http://thepiratebay.se/torrent/6955832/Undergraduate_Math_Te...](http://thepiratebay.se/torrent/6955832/Undergraduate_Math_Textbooks_for_UC_Berkeley)

That would be just a list of title to browse. Buy the ones you find useful.

------
hadoukenio
Naive set theory by Paul Halmos

