What are you reading now? (STEM only)

[Demystifier]

I'd say that some review articles well deserve the status of a book

Here are some of my candidates:

F. Gieres, Mathematical surprises and Dirac's formalism in quantum mechanics, quant-ph/9907069.
It is not so long (56 pages), but the style of presentation is such that it looks like a book chapter.

R. Slansky, Group theory for unified model building, Phys. Rep. 79 (1981) 1-128.
A classic.

T. Eguchi, P.B. Gilkey, A.J. Hanson, Gravitation, gauge theories and differential geometry, Phys. Rep. 66 (1980) 213-393.
Another classic.

 

[vanhees71]

The first one is indeed a masterpiece. The other two I don't know (yet) :-).

 

[cpkimber]

I'm reading through Griffith's Introduction to Elementary Particles. I just got done with my school's equivalent of Modern Physics (though I wouldn't call it simply Modern Physics) and after our few weeks on atomic, nuclear, and particle, I had to know more.

 

[Buffu]

Richard Dawkins - The Greatest Show On Earth
One of his better, more science focused book. He tends often go on about his anti-religious antics from time to time, that even shows up sometimes in his books. Which I don't care about in my opinion, I don't practice a belief system. But for those, like me who just wants to gobble up in science and/or biology in general. This is a great book.

There is an album by Nightwish of the same name inspired by this book of Dawkins. They had Dawkins on stage in Wembley, obviously he did not sing but gave some kind of "prologue".

 

[deskswirl]

Markushevich, Theory of Functions of Complex Variable, 2nd edition
Van Trees, Detection, Estimation, and Modulation Theory, Part I, 1st edition

 

[jasonRF]

Van Trees, Detection, Estimation, and Modulation Theory, Part I, 1st edition

Cool - you are going old-school (but insightful!).

 

[deskswirl]

Cool - you are going old-school (but insightful!).

I thinking about reading Kay's book next. I'm not aware of any other estimation books. Are you?

 

[jasonRF]

I thinking about reading Kay's book next. I'm not aware of any other estimation books. Are you?

Kays book on estimation is good. It focuses on discrete problems (so no integral equations like in Van Trees) and is more straightforward to a non-expert like me.

There are other books:
Scharf, Statistical signal processing (good, but I haven't spent much time with it)
Poor, An introduction to signal detection and estimation (very mathy - you will see measures and integral equations. I'm not a fan but it is popular among some university professors)

Some books on random processes for engineers have some chapters/sections on estimation, depending on what you are looking for: Papoulis (especially fourth edition), Stark and Woods

Jason

 

[Wrichik Basu]

I'm currently reading Introduction to Quantum Mechanics by D. J. Griffiths. I'm a huge fan of QFT, and to master that, I need QM, so I'm reading that now. And seeing working with operators rather than functions can be clumsy.

 

[mathwonk]

i am reading Mumford's "red book" on algebraic geometry. i first perused it 50 years ago but did not really grok it thoroughly. now retired and with time on my hands i want to understand the basics as explained by the great experts.

[seven months later, I am up to page 50, but i have split a lot of firewood!]

[after another 15 months, april 2019, I am now up to page 120. I had no idea there was this much basic information about my subject that I did not know. Makes it somewhat embarrassing in hindsight to think back on all those conversations with people who actually knew the subject. But even now I see questions asked online whose answers are in this book, so not everyone has mastered this source.]

Now that I know how long it takes me to actually read a real book, I am daydreaming about a world wherein all of those prime years in jr high and high school would not have been wasted learning nothing. When I got to grad school I was forced to try to read such books as Spivak's Differential Geometry, and Kodaira and Morrow's Complex Manifolds, in a few days! Someone has to show you which books to read much earlier. Here is a moving article about a man who devoted his career to reaching out to young talents:
\
I got very bogged down in chapter II. section 8, specializations, from all the algebra, but am moving along again now, some months later. Nov. 18, 2019 and I am on page 133 and getting some feel for the ideas of the section. It involves considering a field k and a subring R which is a local ring and maximal for the relation of "dominance" of local rings. If m is the maximal ideal of R, this section discusses how to pass from an algebraic variety over k to one over R and then one over the quotient field L = R/m. One thinks of R as the ring of an infinitesimal curve C with a "fat" dense point a, and a small closed point b. Via the ring maps R-->k, and R-->L, one has maps in the other direction of projective spaces P^n(k)-->P^n(R), and P^n(L)-->P^n(R). There is also a map P^n(R)-->{a,b} so that P^n(k) is the fiber over a and P^n(L) is the fiber over b. Then one specializes an algebraic subvariety Z in P^(k) by mapping it first into P^n(R) and then intersecting it with the closed subspace P^n(L).

By example, one considers a variety over k = Q, defined by integer equations, and the associated integer points of the variety over Z defined by the same equations. Then one reduces it mod p for some prime p, and considers it over Z/pZ = L. The only general result so far is that given an irreducible (hence connected) variety over k, its specialization over L is still connected and of the same dimension.

Ok I finally finished chapter II, ending on p. 136, on December 6, 2019. It was slow but I learned a lot of algebra, including facts about torsion free, flat, and free modules, e.g. although these are consecutively more restrictive conditions in general, they are all equivalent for finitely generated modules over a valuation ring, since every finitely generated ideal in such a ring is actually principal. This gives an idea of the kind of specialized commutative algebra knowledge one needs for this chapter. So I am into my third year of reading this basic book in my specialty, and still enjoying and benefiting from it. Looking forward to the third chapter, on local properties of varieties, which promises to be more geometric. This current chapter was also challenge for me to see the geometry behjind the relentlessly algebraic description, but I learned a few things such as: saying a map X-->Y makes local rings of X torsion free modules over the local rings of Y, means e.g. that no component of X can map into a proper closed subset of Y, since then a function in Y vanishing on that closed subset would pull back to a function that equals zero on X when multiplied by a function vanishing on the other components of X. So the algebraic condition "torsion free" implies the geometric property of density of images of every component. stuff like that takes me time to absorb.

So reading chapter II required several excursions into algebra books, especially in section 4, fields of definition, for bolstering my knowledge of field theory, things like free joins and linear disjointness, and in section 8, for more on module theory, which is also being called on in chapter III.1, as well as localization. So I am taking another hiatus and reviewing bourbaki commutative algebra, chapters 1 and 2 on flat modules and localization.

I am getting a little better feel for tensor products, which have always seemed mysterious. The key properties are that the module MtensN is generated by elements of form mtensn, i.e. consists of linear combinations of them. Then the other key fact is to understand when two such linear combinations are equal, and for that the best thing to keep in mind is the mapping property, that linear maps out of MtensN correspond uniquely to bilinear maps out of MxN. I.e. the whole difficulty is that we like to deal with concrete elements, but it is very challenging in a tensor product to know just when a linear combination is actually equivalent to zero. Moreover it depends on which tensor product the element is considered as belonging to! I.e. in ZtensZ, the element 2tens3 is non zero, but in Ztens(Z/2), it equals zero! Also, even though Z and 2Z are isomorphic, and the element 2tens3 is zero in Ztens(Z/2), it is not zero in (2Z)tens(Z/2) ! The reason of course is that the isomorphism between them takes 2tens3 to 4tens3, which is zero in (2Z)tens(Z/2).

By the way, many people disparage Bourbaki as a text, but just today I found it to be the only adequate resource on my shelf for the algebra facts I needed on flatness. It was not covered in Atiyah Macdonald for instance, and when I turned to Hartshorne for a reference, his first one, Matsumura, dismissed the proof as follows: "the equivalence of properties 1-5 are well known". Thanks a lot. I also did not easily find what I wanted in Eisenbud, so I am gaining an appreciation for Bourbaki, which I also recall was a standard reference even for my great algebra teacher, Maurice Auslander. Eisenbud did have an enlightening remark about the proof of right exactness of tensoring however, which illuminated the somewhat more direct proof given in all other sources. No sources however gave an entirely direct proof, with elements, due to the difficulty above of dealing directly with linear combinations in a tensor product, and knowing just when one is equivalent to zero.

The more Bourbaki I read the more I like it. It gives complete coverage and complete proofs, very clearly exposed with no hand waving or steps left to the reader. This should recommend it to the people here who have said they want detailed explanations that do not leave big gaps for the reader. It also has exercises and even historical commentary. It seems that someone whom prepres in a subject from this source knows everything there is to know about it. Although the authors are anonymous, we know by now that they were all very famous top level mathematicians and this shines through in the quality of the coverage. it should suffice to mention e.g. Weil, Serre, Cartan, Chevalley, Dieudonne', Tate, Eilenberg, Borel, Grothendieck, Lang, Beauville, Raynaud, Samuel...

I wish I had the english translation but the french is also very clear and very easy french for someone with even a basic knowledge of the language. e.g. "commutative algebra" is "alg'ebre commutative", and "flat modules" is "modules plat". "localization" is "localisation". "ring" is "anneau". (think of annulus?)

 

[Buffu]

i am reading Mumford's "red book" on algebraic geometry. i first perused it 50 years ago but did not really grok it thoroughly. now retired and with time on my hands i want to understand the basics as explained by the great experts.

Is algebraic geometry same as analytical geometry ?

 

[mathwonk]

analytic geometry mostly studies geometric figures defined by linear and quadratic equations, in 2 or 3 dimensional affine space over the real numbers. algebraic geometry studies geometric loci defined by polynomials in any number of variables in affine or projective space of any dimension, over any field, as well as abstract versions of these loci defined analogously to manifolds by covering "charts", which themelves can be isomorphic to any affine locus. In particular "singular" points are welcomed, which are points where the locus is not like a manifold but can cross it self or have kinks and folds. In all these cases the functions acting on the loci are polynomials, or derived from them. In abstract algebraic geometry, an attempt is made to further include as rings of "functions" not just polynomials over a field, but any commutative ring with identity whatsoever. In this theory, one starts from such a ring A, and forms the set spec(A) consisting of all prime ideals of A. This is then given a topology in which the "closed" points are the maximal ideals, and prime ideals of coheight r are thought of as subloci of dimension r.

Over the complex number field, the study of geometric loci of dimension one in the "plane" i.e. C^2, or the projective plane and polynomials and rational functions defined on them, is essentially equivalent to the study of one dimensional complex manifolds and holomorphic and meromorphic fuunctions defined on them.

so yes, it starts out a little like analytic geometry, but then you raise the degree and the dimension, and you generalize to more abstract fields and even rings. and you tend not to entertain transcendental functions like e^x, or sin and cos. and although you can imitate differential calculus, it is harder to do integral calculus, although i suppose the complex analytic theory of residue, which you can imitate, gives you a hand in that direction.

as example, the ring R[X] where R = reals, gives a space spec(R[X]) consisting of all prime ideals of R[X], i.e. zero, and all ideals generated by irreducible linear or quadratic real poynomials. If C = complexes, then spec(C[X]) is zero and all ideals generated by linear polynomials X-z where z is a complex number. The ring inclusion R[X]-->C[X] induces by pullback a geometric map spec(C[X])-->spec(R[X]) that is generically 2 to 1, roughly with each pair of conjugate complex numbers mapping to the irreducible real quadratic with those roots, and branched over the "real line" consisting of the maximal ideals of R[X] with linear generators. So from this point of view, the space spec(R[X]) has more information than just the real solutions of real polynomials, it also incorporates Galois orbits of complex solutions. Thus the theory lends itself also to study of number theory.

There are some general analogies with linear algebra, but geared up. Just as one linear equation on k^n defines a linear subspace of codimension one, so (if we assume k algebraically closed) does one polynomial equation on k^n define an algebraic variety of codimension one. More generally, the codimension of the locus in k^n defined by r equations cannot be more than r, in the general case as well the linear case. A surjective linear map from k^m to k^n has all fibers as linear spaces of dimension m-n, while a surjective polynomial map k^m-->k^n has all fibers of dimension at least m-n, and the general one of exactly that dimension.

if you want to begin reading about algebraic geometry, and are really a beginner, a good book is Algebraic Curves, by Robert Walker, or maybe with a bit more algebraic background, Undergraduate algebraic geometry, by Miles Reid. A fantastic book is the huge, scholarly tome: Plane algebraic curves, by Brieskorn and Knorrer. Oh another excellent one is Riemann surfaces and algebraic curves, by Rick Miranda. Bill Fulton has made his lovely 1969 book on curves available for free:

http://www.math.lsa.umich.edu/~wfulton/CurveBook.pdf

Basic algebraic geometry, by Shafarevich, is an excellent introduction to higher dimensional algebraic geometry, i.e. not just curves. All these books are more introductory than Mumford's red book. Mumford's book is of course wonderful, but you will appreciate it more with some background from some of these other books, which have more examples and exercises, and are less abstract.

as a measure of the difference in analytic geometry and algebraic geometry, even in dimension one, note that every (projective) plane curve, over the complex numbers, is a compact surface. those studied in analytic geometry, namely circles, parabolas and hyperbolas, are all (over the complexes) just spheres, whereas those of higher degree are compact surfaces of arbitrary genus g ≥ 0. E.g. plane cubics have genus 1 and smooth plane quartics have genus 3. Indeed defining the genus was a primary contribution by Riemann to the study of plane curves.

The three main theorems about plane curves are the bezout theorem on the number of intersections of two plane curves, the resolution of singularities saying that every plane curve with singularities is the image by a degree one map of a curve having no singularities, and the riemann roch theorem which computes the number of rational functions on a given curve with a given set of poles. all three of these theorems are proved in Walker and Fulton.

generalizing these theorems to higher dimensions have been a primary focus of research for a 150 years or more. The general riemann roch theorem was proved by hirzebruch in the 1950's i think and generalized further by grothendieck in the 1960's. the bezout theorem has been beautifully generalized by fulton in his book Intersection theory, and the resolution of singularities was published by hironaka in 1964 in characteristic zero, and announced by him this year(!) in characteristic p.

http://www.math.harvard.edu/~hironaka/pRes.pdf

 

[mathwonk]

I just realized I may have misunderstood the question about the relation of algebraic to analytic geometry. I understood you to be asking about the elementary subject of "analytic geometry" that is covered say in or before a beginning calculus course of one variable, say the material in George Thomas' Calculus and analytic geometry, or the chapter titled analytic geometry in the book Principles of mathematics by Allendoerfer and Oakley. But today, to a professional geometer, the term analytic geometry means the study of geometric loci in complex space of arbitrary dimension, which are defined by analytic, i.e. holomorphic functions. These also have abstract analogs as complex manifolds, and more generally complex analytic varieties. This is the subject covered for instance in the excellent book Complex analytic varieties, by Hassler Whitney.

The Hirzebruch Riemann Roch theorem mentioned above was proved in the context of complex manifolds, using tools from topology such as cobordism, while that of Grothendieck was in the context of algebraic varieties. Grothendieck had to give an algebraic version of chern classes for his work I believe.

Since polynomials in several variables are a particular type of analyic functions, this means that in a sense, algebraic geometry over the complex numbers is a special case of this broader notion of analytic geometry. Indeed the two subjects overlap significantly, and it was in the 19th century when Riemann introduced complex analysis and topology into the study of algebraic plane curves that algebraic geometry really deepened and started to become the vast subject it is today. Indeed until Riemann introduced topology into the subject, the concept of the genus of a "curve" was unknown. After his work this concept was algebraicized and introduced abstractly in terms of the dimension of the vector space of algebraic differential forms.

I.e. every algebraic plane curve in C^2 inherits a complex analytic structure from its embedding, and Riemann even showed how to remove the singularities from any plane curve and render it into a one dimensional complex manifold, the "Riemann surface" as we call it today, of that curve. A basic theorem is that the field of meromorpic functions on the riemann surface of a plane curve is isomorphic to the field of rational functions of the curve. He also gave an abstract definition of a one dimensional complex manifold and showed that when it is compact, it must arise from an algebraic plane curve, i.e. he gave a way to embed the complex manifold into complex projective space as the locus defined actually by polynomials, from which it could be projected into the plane.

In higher dimensions, even compact complex manifolds need not be algebraic however, since there exist compact complex surfaces, even tori, homeomorphic to the product of 4 circles, that carry no global meromorphic functions at all. For compact complex manifodls that can be embedded complex analytically into the projective space, it can be proved that the image of the embedding is always cut out by polynomials, so that analytically embedded compact complex manifold is actually an algebraic variety, algebrically embedded. It was Kodaira who generalized Riemann's algebraizability result to characterize exactly which compact complex manifolds have such embeddings, they are the ones that carry a sufficiently positive "line bundle", and since such a line bundle is detected by its chern form, it suffices for there to exist a positive integral 2 form of type (1,1), as i recall from distant memory. This is a certain type of cohomology class in H^(1,1);C intersect H^2;Z.

There is a famous paper of Serre referred to as GAGA, Geometrie analytique et geometrie algebrique, in which he shows that for complex projective varieties there is an equivalence of categories between their complex analytic coherent sheaf cohomology theory and the algebraic version defined by their algebraic structure. Sheaf theory was introduced in the mid 20th century as a tool in several complex variables as i recall, and Serre greatly enhanced algebraic geometry by giving an algebraic version of sheaf cohomology in his great paper FAC (faisceau algebrique coherent). Grothendieck then generalized sheaf cohomology further with a more general definition having better exact sequence properties (Serre had used Cech cohomology while Grothendieck used derived functor cohomology).

Having studied several complex variables myself in grad school, and having considered being a complex analyst, (and earlier having studied and contemplated doing algebraic and differential topology), when I returned to algebraic geometry, I brought with me and continued to use the complex analytic and topological tools I had available. So even though I call myself an algebraic geometer, in a significant sense I was really a more of a complex analytic geometer.

 

[Buffu]

@mathwonk I was actually mentioning about the analytical geometry that is taught with calculus but your second post was also worth mentioning. Is differential geometry a subset of algebraic geometry ? My geometry knowledge approximately zero. I know plane geometry taught in school and a bit of conic sections.

I will read the book Reid's book after learning a bit of linear algebra.
Thank you for all the books.

 

[mathwonk]

differential geometry includes a notion of length which is not part of algebraic geometry. the concept of curvature however seems to coexist in both in some form. Some of my friends did some work on the behavior of curvature on plane curves I believe, in particular Linda Ness.

Apparently there is a natural metric one can use on algebraic curves in affine or projective space, the :"Fubini - Study" metric, and one can then study differential geometric properties of algebraic varieties. Here is a part of Linda's thesis done under the direction of the famous algebraic geometer David Mumford.

http://www.numdam.org/article/CM_1977__35_1_57_0.pdf

 

[martinbn]

Differential geometry doesn't always include a notion of length. That's what one has in Riemannian geometry or Finsler geomtery. On the other hand differential geometry is not a subset of algebraic geometry, nor is algebraic geometry a subset of differential geometry.

 

[Demystifier]

Differential geometry doesn't always include a notion of length. That's what one has in Riemannian geometry or Finsler geomtery. On the other hand differential geometry is not a subset of algebraic geometry, nor is algebraic geometry a subset of differential geometry.

Would you agree that one particular book on algebraic geometry, namely Griffiths and Harris
https://www.amazon.com/dp/0471050598/?tag=pfamazon01-20
is actually a book on differential geometry?

 

[martinbn]

Would you agree that one particular book on algebraic geometry, namely Griffiths and Harris
https://www.amazon.com/dp/0471050598/?tag=pfamazon01-20
is actually a book on differential geometry?

Not quite, the methods used to study the geometric objects are mainly algebraic, hence algebraic geometry. On the other hand I would agree with you as they study complex manifolds (that often happen to be complex varieties). May by it should be classified as complex geometry (or complex analytic geometry). But I have only looked at the book, never read it so I can be persuaded either way.

 

[mathwonk]

Griffiths looks at algebraic varieties, always over the complex numbers, through the lens of complex manifold theory. His main tools are drawn largely from complex analysis of several variables. In that book he and Harris first develop foundational results for complex manifolds such as the Kodaira vanishing theorem, and the Hodge decomposition, and then apply them to the study of complex projective varieties. They also employ topological tools like Poincare duality, and later introduce and apply spectral sequences. The discussion includes some theorems generally included within the realm of differential gometry, such as a generalized version of the Gauss Bonnet theorem, apparently in the version due to Chern, a famous complex differential geometer. There is also some discussion of the Hirzebruch Riemann Roch theorem. Griffiths and his school are primary contributors to the field of Hodge theory, the study of cohomology of manifolds, especially algebraic ones, via the decomposition of their cohomology by harmonic differential forms. He has several seminal papers on periods of integrals, generalizing theories of Riemann and Abel and Torelli. Here is a link to his ICM talk from 1970 describing some of these ideas and their origins in the analytic theory of curves.

http://www.mathunion.org/ICM/ICM1970.1/Main/icm1970.1.0113.0120.ocr.pdf

I myself would say his work is within algebraic geometry because it studies algebraic geometric objects, but would consider the methods as differential analytic. I.e. I think of complex algebraic geometers as tending to study complex algebraic varieties with any methods available, algebraic, analytic, or topological. This was apparently the path pioneered by Abel and Riemann. By contrast, for a treatment of algebraic curves using only algebraic methods, such as integral ring extensions, see the book by William Fulton linked above (post 47).

I realize now that I have been somewhat cavalier about what context I am working in from time to time. Here is one of my papers in which it is stated that the field can be any algebraically closed one of characteristic ≠ 2, hence all methods must be algebraic.

http://alpha.math.uga.edu/%7Eroy/sv5rst2.pdf

and here is one where the field is restricted to the complex numbers:

http://alpha.math.uga.edu/%7Eroy/sv2rst.pdf

Here is another where the field must be the complex numbers, but that is not even stated.

http://alpha.math.uga.edu/%7Eroy/sv1nr.ps

Note also that Griffiths, in the 1970 talk linked above, speaks only of algebraic geometry, no mention of complex algebraic geometry, yet he immediately begins to write down complex path integrals.

I just noticed I myself wrote a brief essay "introducing" algebraic geometry to a class of graduate students taking the course, in case someone may get something from it:

http://alpha.math.uga.edu/%7Eroy/introAG.pdf

By way of disclosure, Griffiths is my mathematical "grandfather", in the sense that he advised my thesis adviser, C.H. Clemens.

 

[davidge]

This semester, I've to create problems for a GR/cosmology lecture. So I'm right now reading a bit in the literature. Whenever there's something unclear, I turn (of course) to

S. Weinberg, Gravitation and Kosmologie, Wiley&Sons, Inc., New York, London, Sydney, Toronto, 1972.

If I had to make a list of books on this topic I would put that at the end. No, in fact I will not put it in the list.

Why?

 

[mathwonk]

to give an example of the very concrete questions that still puzzle us in algebraic geometry, even after the vast strides made by the giants of the last 150 years, consider the question of which algebraic varieties can be parametrized by affine space. we call two varieties birational if they have isomorphic rational function fields, or equivalently if they have isomorphic (large) open subsets. An n dimensional variety V is called rational if it is birational to affine space k^n, i.e. if there is a generically injective map k^n--->V defined by rational functions, with dense image. then it is a non trivial problem to show that a smooth plane curve is rational if and only if its degree is ≤ 2. It is easy to show a variety of degree ≤ 2 is rational, since deg 1 means it is actually isomorphic to affine space, and deg = 2 alows us to project from one point, generically bijectively to affine space. the 19th century geometers knew that smooth surfaces in P^3 are rational if their degree is ≤ 3. A cubic surface V e.g. contains lines, and if L,M are two of them, then for each pair of points (x,y) on LxM, the line in P^3 joining x and y meets V further at one point in general. This sets up a generically bijective correspondence between V and LxM ≈ k^2, so V is rational. It took over another 100 years to prove that no smooth cubic 3 fold in P^4, e.g. X^3 + Y^3 + Z^3 + W^3 = 0, is rational and the first proof in 1972 used a lot of topology, geometry, and analysis, including the theory of principally polarized abelian vaieties (complex analytic group varieties). If we consider a smooth 4 fold W in P^5 that contains two 2 - planes, the same argument shows that W is birational to k^2 x k^2 ≈ k^4, hence rational, but most smooth cubic 4 folds do not contain such planes, and it is still unknown today whether some smooth cubic 4 fold might be irrational! So we don't even know how to recognize when a very specific hypersurface in P^5 is essentially the same as affine space!

An even simpler problem is to decide whether every irreducible curve in 3 space, either affine or projective, is the set theoretic intersection of just two surfaces. Still open to my knowledge at least in projective space.

 

[zzzhhh]

I'm now reading "Vector and tensor analysis", Louis Brand, 1948, together with some other books that refresh my mathematical foundations.

 

[PSRB191921]

Hi
I am reading Applied Physics of External Radiation Exposure Dosimetry and Radiation Protection (springer 2017) https://rd.springer.com/book/10.1007/978-3-319-48660-4
If you want to calculate radiation Dosimetry quantities for photons, neutrons, electrons, beta, secondary particles ( photonuclear, Bremsstrahlung, ...) you must read this book. Also it helps me for calculating shielding of different devices ( x-rays generator, accelerator, fusion, fission, ...)
PSR

 

[Salvador Sosa]

I'm reading the fundamentals of physics by r Shankar

 

[enrev91]

Axler's Linear Algebra Done Right. I love it.

 

[Buffu]

Axler's Linear Algebra Done Right. I love it.

He hates determinants. Think twice before using that book.

 

[enrev91]

He hates determinants. Think twice before using that book.

I'm taking a university course next semester that'll use determinants. So no worries-- I'm seeing both approaches.

 

[mathwonk]

i suggest using shilov as a counterpoint/supplement to axler.I don't know if it speaks to anyone else, but I also benefited from writing my own linear algebra notes:

http://alpha.math.uga.edu/%7Eroy/laprimexp.pdf

This is an expanded version of my 15 page linear algebra book posted here some years ago, ratcheted up to over 125 pages. Basically instead of trying to make it as short as possible, this time I took my experience teaching bright youngsters to try to make it understandable. But the fact that it is still 1/2 or 1/3 the length of other books suggests it maybe still goes too much straight to the jugular. So probably it is recommended to someone who thinks he/she already knows the subject. I.e. I studied and taught the subject for years, and this is my take on it after rethinking it again for some years lately. So i suggest that if you think you already know linear algebra, as I thought i did, see if this treatment does not still challenge you a bit. If anyone does so, please let me know, (we authors get so little feedback and we need so much).

 

[scottdave]

Eight Amazing Engineering Stories: Using the Elements to Create Extraordinary Technologies, by Bill Hammack

 

[ElectricRay]

The legendary book Cosmos from Carl Sagan, nice book even though its a bit old.

 

[Zurvan]

Reading and going through Quantum Field Theory for the Gifted Amateur by Lancaster and Blundel. So far it has been very enjoyable.

 

[Coelum]

What book are you reading now, or have been reading recently? Only STEM (science, technology, engineering and mathematics) books are counted.

Melvin Schwartz's "Principles of Electrodynamics" -

 

[automotiveadam7]

Been cooking on "Basic Electricity", a "Reprint of the Bureau of Naval Personnel Training Manual". It's almost too thorough in some areas, but I'm likin' it.

 

[DS2C]

Algebra by Gelfand/Shen and Understanding Physics by Isaac Asimov

 

[Dr Transport]

Scattering of Electromagnetic Waves From Rough Surfaces, Beckman and Spizzchino...(for a new job coming in the next month or so)...