Hardest upper undergraduate pure maths subjects?

[mathwonk]

spivak is not an analysis book, it is only called one by people who have elarned calculus without any theory, it is a beginning calculus book with theory.

but if you do not know the stuff in spivak, it is a good place to start.

for intro to analysis, i recommend simmons. it seemed clear to me back in 1970 when i first encountered it.

rudins real and complex book is an advanced analysis book, excellent, but based on what to me is a flawed premise, that real and complex analysis are closely entertwined and should be learned together.

i myself find them to have very different flavors.

but do not be afraid to look at any book, no matter who says it is ahrd. you have tod ecide for yourself what book is right for you.

i once avoided reading the book homological algebra for years, by cartan and eilenberg because someone told me it is was hard, only to find it extremely clear and easy to read.

when i told the person, they checked their sourcde and had actually misunderstood the assertion, it was that the book seemed "tedious" to someone else, which is often another way of saying carefully written and detailed.

 

[InbredDummy]

But probability is an intrinsically applied maths subject. Just like Quantum Mechanics is intrinscially applied. It happens that there is an abstract formalism of QM but does that make QM a pure maths subject?

until you have taken a pure math probability theory course and a measure theory course, we can't really have this discussion.

 

[hockey777]

Combinatorics was my hardest.

 

[mathwonk]

our students do worst in analysis, hands down. possibly because we used rudin's very user unfriendly book.

 

[Coto]

quasar987,

Meh, I'm third year and I haven't taken nor intend to take any time soon, a single analysis course. I did do Metric spaces, however.

By the way, sorry to be a thread imposter but no one gave me any advice on my last post. Who can rate these in descending order of usefulness/importance in theoretical physics?

Functional analysis
Partial differential equations
Algebraic topology
Algebraic geometry
Commutative algebra
Representations of the symmetric group

(n.b. they are all at fourth year pure maths level)

I'm doing my masters in applied mathematics (undergrad in physics). This is just my experience when dealing with analytical mechanics.

Functional Analysis - Gives fundamental results that will really help benefit your understanding of PDEs.

Partial differential equations - Almost every fundamental physical equation is a PDE of some kind and at some level. The draw back of PDEs is their dependence on a coordinate system, which as you can guess becomes a problem when dealing with subjects such as GR.

As a side note, welcome to Tensor Analysis, Differential Geometry...

Algebraic Topology - Haven't encountered anything further than an introduction to topology, and haven't needed anything further or seen any higher physics using it.

Algebraic Geometry - Likewise.

Group Theory - Probably the most useful of algebraic abstractions for physics. Lie groups, symmetric group, fundamental results relevant to particle physics, analytical mechanics, quantum mechanics...


Hope this helps.

 

[CompuChip]

<offtopic> Wow, isn't October 16, 2008 a beautful day to resurrect a thread, which was last posted in July 1, 2007. </offtopic>

 

[sportsstar469]

hey i have a question. what are the names of math courses that are well above the undergraduate level? like what courses do phds in maths take? I've heard algebraic topology is hard also./

 

[CompuChip]

<offtopic> Wow, isn't October 23, 2009 a beautful day to resurrect a thread, which was last posted in October 16, 2008. </offtopic>

 

[lubuntu]

lol!