The completion of my undergraduate degree merely cries out for a post about some of the books that helped me survive these last few years. There exists a plethora of educational texts on *any* possible topic within maths or physics, which could easily overwhelm students (especially first years) and prevent them from as much as stepping a foot in the university library. I know, because I, too, was initially utterly overwhelmed at the sheer amount of knowledge contained in the countless bindings of pages on the bookshelves.

It can be so easy and tempting to just always refer to some internet forum for an answer, but as fast and (usually, albeit not always) useful as the content on the WWW is, one might discover a lot of **utter** junk that is bound to a) confuse you even more, b) be aimed at the wrong level of expertise, c) be written by some troll who will make you feel like an idiot for asking a seemingly trivial question, and d) lure you into the darker corners of the internet, brimming with temptations to procrastinate. A quick search for an explanation of the Pointing Vector may well turn into a half-hour episode of funny cats, John Oliver or Zoella….

Today, I want to share a collection of texts that * I *have found incredibly helpful throughout my degree and talk about the importance of consulting some classic texts when you are stuck for an explanation of a concept. Some of these are more general texts, whilst others are geared towards a specific module; some would have appeared as “recommended textbook” for a particular course, whilst others were found on a whim from my curiosity.

Many of these might be searchable for a pdf download (at least definitely the ones I have starred!) and also bought cheap as chips second or third or hundredth-hand on **www.abebooks.co.uk .** I did not want to breach any copyright issues, hence no direct links to free pdf’s – but Google is your friend for the titles with the star!

I’ll begin with a more general piece which single handedly saved not only my degree, but also my sanity back in first year…

– L. Alcock, **How to study for a mathematics degree. **

This is a text (quite obviously) geared towards mathematicians, but any science student would benefit because it offers some indispensable guidance on how to not only go about revising for exams, but also how to manage your weekly uni life in general so as not to drive yourself insane from the abundance of blackboards and chalk and neverending assignments. Lara Alcock, who currently teaches at Loughborough University, provided me with a means of reviving my crumbling self-confidence after performing atrociously on my first ever mathematics exams (one of which I did actually fail by *one* mark despite solid preparation; something I am still quite ashamed of). I was terrifyingly close to dropping out at this point and starting afresh next year. What I was not aware of at the time, was that **the majority **of students were equally as shocked as me at the difference between their marks in A-Level exams, and those they received upon sitting their first undergraduate mathematics exams. There are few things more mentally unsettling than witnessing your previous exam scores of >93% suddenly swapping the digits back to front.

It took a book like this for me to realise that I felt like an inadequate idiot only because I happened be in the vicinity of some super smart students. In reality, I was not, and am not, an inadequate idiot. I was merely below average in the couple of modules that happened to be examined first. I thank Laura Alcock, and the person who recommended me her book, for helping me find self-courage and light at the end of this three-year-long tunnel.

2*. **H D Young and R A Freedman, ****University Physics, (**Pearson).

Bulky enough to serve as a doorstop when not in use, this textbook covers pretty much everything in the first two years of a physics UG degree at just the right level. It satisfies the hunger, but is not quite sufficient to learn any particular topic in greater depth. It is, for this reason, a frustrating read – but at least it comes with lots of exercises and the bane of a fresher’s life: that dreaded weekly online Mastering Physics assignment….

3. **M. Spivak, Calculus,** (Benjamin).

A big and bulky mathematician’s bible. Along the same lines of Analysis are also:

- M. Hart,
**Guide to Analysis**, (Macmillan) – provided me with some beautiful epiphanies, where I finally understood limits…. Currently super expensive on Amazon, and no cheap copies going on abebooks.co.uk BUT you can ask me nicely and I may choose to pass my copy onto a new, loving owner… - * P. Walker,
**Examples and Theorems in Analysis, (**Springer) – a snazzy collection of Analysis I, II and III all combined into a neat package of 282 pages. With examples, more examples and… examples. Maths is not a spectator sport, after all.

4. W A Sutherland, **Introduction to Metric and Topological Spaces,** (OUP)

This became a bedtime read during my summer between years 1 and 2. Glad it mentions Topological Spaces, as opposed to the title of the module (“Metric Spaces”) here at Warwick, which fails to warn the poor student that only about 10% of the module matches this title; whilst the remaining 90% is, indeed, Topological Spaces.

Alternative to the book, **here** is a very handy series of lecture notes by Korner from Cambridge.

5*. K.F Riley, M.P. Hobson, S.J. Bence, **Mathematical Methods for Physics and Engineering**, (CUP)

Perfect example of why I think turning to a book to understand Fourier transforms is much better than turning to the WWW. Triple integrals, spherical and cylindrical coordinates, some ‘illegal’ and wishy-washy mathematics… all to be found in this doorstop for the door not already supported by the University Physics textbook!

6. F. Mandl, **Quantum mechanics**, (Wiley 1992)

I never try to suppress the quantum nerd inside me, so it was only a matter of time before a quantum book made it onto this list! Mandl’s text explains things *really *well, and it served me for both years 2 and 3 quantum modules. Apparently not a standard textbook, but the quantum textbook of my choice…. closely followed by the **Feynman Lectures on Physics vol. III, **and the one which made my final year project bearable: **Quantum Information and Quantum Computation **by M.A. Nielsen, I.L. Chuang.

7*. D. J. Acheson, **Elementary Fluid Dynamics,** (OUP)

Keep this on the quiet, but I actually quite liked my Fluid Dynamics module, and this beautiful little text may have influenced this. Evidently a massive fan of Navier and Stokes. Explains lots of confusing concept in a succinct manner and comes with lots of example questions (and model solutions) to help prepare for that exam.

8. JFR McIlveen, **Fundamentals of Weather and Climate,** (2nd Ed, Oxford, 2010)

Weather nerrrrrd unite! The weather module would have been my favourite module, if it hadn’t been taught in the most boring way possible. So this is where I supplemented the sleep-inducing lectures with various youtube videos and textbooks such as this one and also **The Atmosphere and Ocean: A Physical Introduction, **by N. C. Wells (Wiley and RMetS).

9*. S. Simon, **The Oxford Solid State Basics, ** (OUP, 2013)

A book which covers the entirety of the Solid State Physics module, as given at Oxford by Prof. Simon. An incredibly comprehensive read, with a series of video lectures on the Oxford website, with a few terrible jokes to make your heart crumble a little. But it saved my socks for the exam, so **go go go!**

So: here is my shortlist, though many other texts have been consulted over the few years, with many more to come in the future I am sure! Don’t ever be afraid to search out helpful resources in the library or on the net, but take the latter with a pinch of salt. Feel free to message me or comment here with more suggestions of books which you may have found indispensable – be it studying physics, mathematics, or any other science.

Over ‘n out 🙂

A book that saved me as a mathematics undergraduate was … I don’t actually know. But I was struggling in Real Analysis, as many do, and grabbed a book from the library at what might as well have been random to try to save myself. I got one in French, which I had studied in middle and high school but couldn’t really read fluently.

And I think that made a difference, actually. I could follow the lines of an argument all right, with difficulty. That so much technical language is in common between French and English meant it wasn’t

thatforeign. And I think having to take the time to parse each sentence independently kept me from skimming the stuff I had to not skim.I’m not saying I came out

well,but I avoided a complete route in the class. I wonder what book it was.Hi Joseph, thanks for your comment! It’s interesting to note that you didn’t simply put the book down after realising it was in a different language altogether. But that’s just it; the technical vocabulary tends to be quite similar in various languages and of course equations speak their own, universal language! I’m quite certain that luckily, epsilons and deltas and ‘lim’ are the same, wherever you go.

It is a shame you never found the book again, though.

When I studied my undergrad in physics, from day 1 the lecturers told us to get two books that would help in almost every circumstance that turned out to very useful:

1) Engineering Mathematics – K. A. Stroud (Amusing name for a physics degree). This was by far a life safer on understanding much more complicated maths not taught at A Levels and the book was great as it didn’t preach maths in the typical boring dullness of a textbook, but in a more interactive numbered step by step progression with answers and solutions at almost every step. I’m not a massive reader myself, but nevertheless I managed to read almost the entire 1300 page book, because being a nerd it was actually quite fun!

2) Physics for Scientists and Engineers with Modern Physics – Tipler and Mosca. Just like so many science/maths books of this shear size, this caught everyone’s attention in the library when you placed it on the desk in front of you. This really helped explain a lot of key principles on all areas of physics for the first or second year that the lecture notes couldn’t. When wanting more detail of quantum mechanics and astrophysics a more comprehensive book was needed. This reminded me very much of A Level Physics through their long explanations and then questions (and luckily with well described solutions).

I’ve managed to read (parts) of a lot of books, but usual their very size and nature makes finishing any of them very painstaking. Although one book that did come to mind which was more useful than the others:

3) Elementary Climate Physics – F. Taylor. This was very useful because it was tailored to the physics and maths side of science and would jump straight into explaining the importance of why having a mathematical/physical description was so important. The way they explained many concepts with lots of equations was very useful in understanding the basics of climate sciences. Tied close to this book was: Atmospheric science: an introductory survey – Wallace and Hobbs.

This pretty much sums up most of the useful books I’ve encountered in my UG days. Sorry if this was long winded.

Hi James, thanks for sharing your choices! Not long winded at all. It’s interesting you point out the “shear size” of Tipler and Mosca – it sounds like one of those all-rounders but without the detail. Those textbooks can be useful, but so very annoying in that aspect. I have definitely used the Climate Physics one by Taylor, but not the one by Wallace and Hobs. I might look into it.

I’d say that a

goodtextbook would be one to not only explain the main concepts, but also provide questions – and possibly a handbook of hints / suggested / partial solutions, but without giving a 100% complete bank of solutions! It’s nice if the author helps you actuallythinkabout the solution to the problem, rather than just handing it to you on a plate, which so many books do.When I studied my undergrad in physics, from day 1 the lecturers told us to get two books that would help in almost every circumstance that turned out to very useful:

1) Engineering Mathematics – K. A. Stroud (Amusing name for a physics degree). This was by far a life safer on understanding much more complicated maths not taught at A Levels and the book was great as it didn’t preach maths in the typical boring dullness of a textbook, but in a more interactive numbered step by step progression with answers and solutions at almost every step. I’m not a massive reader myself, but nevertheless I managed to read almost the entire 1300 page book, because being a nerd it was actually quite fun!

2) Physics for Scientists and Engineers with Modern Physics – Tipler and Mosca. Just like so many science/maths books of this sheer size, this caught everyone’s attention in the library when you placed it on the desk in front of you. This really helped explain a lot of key principles on all areas of physics for the first or second year that the lecture notes couldn’t. When wanting more detail of quantum mechanics and astrophysics a more comprehensive book was needed. This reminded me very much of A Level Physics through their long explanations and then questions (and luckily with well described solutions).

I’ve managed to read (parts) of a lot of books, but usual their very size and nature makes finishing any of them very painstaking. Although one book that did come to mind which was more useful than the others:

3) Elementary Climate Physics – F. Taylor. This was very useful because it was tailored to the physics and maths side of science and would jump straight into explaining the importance of why having a mathematical/physical description was so important. The way they explained many concepts with lots of equations was very useful in understanding the basics of climate sciences. Tied close to this book was: Atmospheric science: an introductory survey – Wallace and Hobbs.

This pretty much sums up most of the useful books I’ve encountered in my UG days. Sorry if this was long winded.