How to prepare for Theoretical Physics MSci over a gap year?

[KingCrimson]

So I will be starting an undergraduate MSci degree in Physics/Theoretical Physics in 2017, for the time being I am on a gap year. What's the best way to mentally prepare for a theoretical physics degree? I am not just talking about being familiar with the topics discussed, but also improving my problem solving skills as much as I can.
I will be doing the STEP papers (extra hard maths papers in the UK), which are quite challenging from what I have heard. I will also work through all the mathematics/physics Olympiad papers. I will go through all the Maths modules I did not do in my A-Levels. I am also learning Python.
Any tips? Any challenging books to read that could improve my problem solving skills?Any skills that you think might be useful?
Thanks in advance.

Note that I am aiming for getting at least a first (70%) over the 4 years at one of the toughest universities in the UK in terms of examinations.

 

[KingCrimson]

Any help, guys?

 

[bolbteppa]

At a base level, learn about and then try to do the first year syllabus, the homeworks and the end-of-term exams from previous years from the course websites, learn LaTeX, mathematica, c++ programming. Beyond this, for starters, do your best to learn things like calculus (Thomas/Stewart), multivariable calculus (Thomas/Stewart), vector analysis (Schey), linear algebra (Anton), discrete math (no idea), elementary differential equations (Tennenbaum), elementary real analysis (Mendelson), elementary topology (Munkres), elementary manifold theory (Shifrin), intro calculus-based physics (Halliday-Resnick), Newtonian mechanics (Kleppner), elementary electromagnetism (Purcell), elementary special relativity (intro GR book early chapters, e.g. Ryder), elementary calculus of variations (some equations of math physics book), elementary tensor analysis (intro GR book early chapters) and (very slowly) prep for 2nd year subjects, youtube lectures for every topic online, e.g. Shifrin https://www.youtube.com/channel/UCp9W-et2Zbx7u5_VMiXGtPQ treat olympiad stuff as extra-curricular, step (from vague/bad recollection) is a bunch of hard problems from those calculus books and some linear algebra and discrete math and stats.

 

[KingCrimson]

At a base level, learn about and then try to do the first year syllabus, the homeworks and the end-of-term exams from previous years from the course websites, learn LaTeX, mathematica, c++ programming. Beyond this, for starters, do your best to learn things like calculus (Thomas/Stewart), multivariable calculus (Thomas/Stewart), vector analysis (Schey), linear algebra (Anton), discrete math (no idea), elementary differential equations (Tennenbaum), elementary real analysis (Mendelson), elementary topology (Munkres), elementary manifold theory (Shifrin), intro calculus-based physics (Halliday-Resnick), Newtonian mechanics (Kleppner), elementary electromagnetism (Purcell), elementary special relativity (intro GR book early chapters, e.g. Ryder), elementary calculus of variations (some equations of math physics book), elementary tensor analysis (intro GR book early chapters) and (very slowly) prep for 2nd year subjects, youtube lectures for every topic online, e.g. Shifrin https://www.youtube.com/channel/UCp9W-et2Zbx7u5_VMiXGtPQ treat olympiad stuff as extra-curricular, step (from vague/bad recollection) is a bunch of hard problems from those calculus books and some linear algebra and discrete math and stats.

What do you think of reading Spivak's Calculus? I have already done A-level maths and further maths so I have studied a lot of calculus (not much real analysis though).

 

[bolbteppa]

Treat Spivak as elementary real analysis, do all/most-of the problems and proofs from the big bumper Thomas/Stewart calculus books, especially the later multivariable calculus chapters, will extremely help.

 

[KingCrimson]

Treat Spivak as elementary real analysis, do all/most-of the problems and proofs from the big bumper Thomas/Stewart calculus books, especially the later multivariable calculus chapters, will extremely help.

I will read them both. I have been recommended reading Axler's Linear Algebra Done Right, what do you think? Is it better than Anton's? I am looking for the more theoretical option.

 

[bolbteppa]

Yeah Axler is great, probably the best on the material it does, but if you want 70%+ I'd say do all the Anton theory/problems as well.

 

[Crek]

Spivaks calculus book is stupid to use if you already known calculus, use a proper advanced calculus textbook or elementary analysis book.

Axlers book is Ok, I own it but honestly I prefer Friedberg as it provides information in a more standard fashion.

 

[micromass]

Spivaks calculus book is stupid to use if you already known calculus, use a proper advanced calculus textbook or elementary analysis book.

Axlers book is Ok, I own it but honestly I prefer Friedberg as it provides information in a more standard fashion.

Uuh, what advanced calculus book would be better than Spivak?

 

[George Jones]

Uuh, what advanced calculus book would be better than Spivak?

Which book by Spivak, "Calculus" or "Calculus on Manifolds"?

 

[micromass]

The thread has been talking about Spivak's calculus.

 

[George Jones]

The thread has been talking about Spivak's calculus.

Okay. The reason I asked is because Crek wrote

if you already known calculus, use a proper advanced calculus textbook or elementary analysis book.

and, in North America, "advanced calculus" often means mutivarible/vector calculus (e.g. the book "Advanced Calculus" by Taylor and Mann that was used as the text for a course that I took), but Crek could have meant something different than this.