youwen5/alexandria
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions 1

auto-update(nvim): 2025-01-17 15:24:05
Some checks are pending
Deploy Quartz site to GitHub Pages using Nix / build (push) Waiting to run
Details
Deploy Quartz site to GitHub Pages using Nix / deploy (push) Blocked by required conditions
Details

Browse source
This commit is contained in:
Youwen Wu 2025-01-17 15:24:05 -08:00
parent ab73cfe5c7
commit ed5a3e5215
Signed by: youwen5
GPG key ID: 865658ED1FE61EC3
1 changed files with 13 additions and 1 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

14
documents/by-course/math-8/course-notes/main.typ
View file

@ -17,8 +17,18 @@
#outline()
= Introduction
Math 8 is an introductory course on mathematical logic and the methods of
proof. In general it will be quite trivial for anyone somewhat familiar with
competition mathematics or proofs. If you are at UCSB, I highly recommend you
take this course as soon as possible to unlock the rest of the higher
mathematics offerings here (which are much more interesting).
= Course Logistics
Everything in this section is information only valid for the Winter 2025 quarter with Professor Porter.
The textbook for the course is _Smith, Eggen, Andre. A Transition to Advanced
Mathematics. 8th ed_. #smallcaps[isbn:] `978-1-285-46326-1`. Chapters 1-5 will
be covered.
@ -315,13 +325,15 @@ $ P => Q and Q => P $
then showing that this fact leads to a contradiction.
A proof by contradiction of $P => Q$ proceeds by assuming $P and not Q$, then
showing a contradiction, implying that $P$ indeed implies $Q$.
showing a contradiction, forcing that $P$ indeed implies $Q$.
]
#definition[
A real number $x in RR$ is called rational iff
$ exists p,q in ZZ, x = p / q $
]
#definition[
$x$ is irrational if it is not rational.
]