A guide to math textbook titles
I decided to create the following simple guide to math textbook
titles. Who knows, it might be useful to any undergrads out there :)
Anyone who wants to add to the list or change it, feel free :)1. (TOPIC) for Scientists and Engineers
What Mom would think: Wow! This must be super-difficult!
True translation: The definitions are pure hand-waving.
There are no proofs. Some theorems are actually
false in degenerate cases. Light reading.
2. (TOPIC)
What Mom would think: Tough call, but a good chance
this book is medium-hard in difficulty.
True translation: Tough call, but a good chance this
book is medium-easy in difficulty.
3. Topics in (TOPIC)
What Mom would think: Medium-easy. Armchair reading.
True translation: Difficult. Probably graduate level.
Probably has dozens of open problems mixed in the
exersizes.
4. Introduction to (TOPIC)
What Mom would think: Introductory. Meant for freshmen,
or maybe advanced high school seniors. Boringly easy.
True translation: Tough call, but a good chance this
book is hair-pullingly, agonizingly difficult. A
good rule of thumb: if the "preliminaries" section
goes from naive set theory to functional analysis in
one page, you may be in over your head.
5. Lecture notes in (TOPIC)
What Mom would think: Cursory and simple. No proofs.
Some definitions hand-wavey. Very easy. Good last
minute review before the big exam.
True translation: If you can decrypt this arcane tome,
we'll give you an honorary Ph.D. Slight risk half
the book is in Russian or Hungarian. Not that you'd
probably notice the difference!
Some special cases:
"Advanced Calculus" - a wildcard. Can denote just about anything. I
once bought a book called "Advanced Calculus" and it turned out to be
an Afghani cookbook. Back in undergrad days we used to gamble with
these: place bets on what it's about. I won $20 once this way.
"Modern Algebra" - a highly polarized wildcard. There is a 50/50
chance it's a 7th grade book that'll teach you how to solve "4x+7=2"
and a 50/50 chance it'll reach Lie algebras in the first 15 pages.
"(TOPIC) for the Working Mathematician" - contrary to the title, this
book is not meant for anyone but a math hermit who is prepared to
devote the next 20 years to reading it.
"Chaos Theory" - this book will be very rigorous up to about Lyapunov
exponents. Then the last 4 chapters will be a prolonged whine about
how nobody can agree on a good definition of chaos and even if they
could it's all beyond the scope of this text... ooohh look, pretty
fractals! Much hand-wavey allusion to weather systems without any firm
details. A good read if your sole purpose is to impress laymen.
"Conference Proceedings" - if the equations are handwritten, forget any hope
of understanding. Often found at 2nd hand book shops. A particular favourite
of mine is 'Volume VIIa, Lorentz Group' (so what about the first six
volumes?), Lectures in Theoretical Physics, Univ. Colarado, 1964. I reckon
Einstein walked out of this conference cos it got too much. Mom would tell
all her neighbours. Great on the shelf, until someone in the know actually
quizzes you about it.
"Topological Algebras" - forget it. Throw up a toy set of mathematical
symbols, re-arrange into a line. You will probably understand the resulting
equation more than anything in said topic book.
"A first course in..."
"Elementary .."
"For the laymen .." Simple unless it is written by Penrose - his laymen are
all well-respected Physics lecturers
Undergraduate Series in Mathematics: (TOPIC)
What Mom would think: Oh how nice! A pretty little yellow textbook
with homework problems for one of your classes.
True Translation: Might as well leave out the "Under", most of them
are as difficult as the "Graduate Series in Mathematics" texts and the
odds of one of these books actually being used in your average
undergraduate program are about the same as the odds of your mom
understanding even the first page.
Source:
http://jcdverha.home.xs4all.nl/scijokes/1.html