If you believe your copyrighted material appears in this deck without permission, please contact me at [email protected] with details, and I will promptly remove it upon request.

====================================================

This deck contains everything taught in UIUC's MATH 213 - Basic Discrete Math course that I took (I included additional sections on number theory as well).

The course is based on the textbook Discrete Mathematics and Its Applications by Kenneth H. Rosen

Download the version of this deck that has images for free on kofi.

⭐️ Features ⭐️:

Cards in the deck contain plentiful context on the back so that you can "look up" stuff you don't understand.
Every card is color-coded and math is written in MathJax
Every card is thoroughly tagged by their chapter and topic.
The cards in this deck work with the Clickable Tags addon.
All cards are ordered so that material that comes earlier in the course shows up as new cards before material that comes later.

📖 Contents of the deck, organized by tags 📖:

contents

❤️ Support 😊:

Has my deck really helped you out? If so, please give it a thumbs up!

Please check out my other ✨shared decks✨.
To learn how to create amazing cards like I do, check out my 🍒 3 Rules of Card Creation

Sample Data

Text	If \(f:A\to B\),we say that set \(A\) is the {{c1::domain}} of \(f\) and set \(B\) is the {{c1::codomain}} of \(f\).
Replace
Answer
Attached
Overlapping
Subject Clozes
Deck ID	857020437
Summary 1
Back Extra	If \(f (a) = b\), we say that \(b\) is the image of \(a\) and \(a\) is a preimage of \(b\).The range, or image, of \(f\) is the set of all images of elements of \(A\).Also, if \(f\) is a function from \(A\) to \(B\), we say that \(f\) maps \(A\) to \(B\).
Summary 2
Back Extra 2
Summary 3
Back Extra 3
Summary 4
Back Extra 4
Summary 5
Back Extra 5
Summary 6
Back Extra 6
Summary 7
Back Extra 7
Summary 8
Back Extra 8
Summary 9
Back Extra 9
Summary 10
Back Extra 10

Text	Regarding a linear congruence of the form \(ax \equiv b \pmod m\) where \(m>1\),if {{c1::\(a\) and \(m\) are relatively prime::condition}}, then {{c2::a "unique" \(\overline a\), inverse of \(a\) modulo \(m\), exists::what is true}}.
Replace
Answer
Attached	"unique" as in unique modulo \(m\) because any \(\overline a+km\) is also an inverse.2 numbers are relatively prime if their \(\gcd\) is \(1\)
Overlapping
Subject Clozes
Deck ID	857020437
Summary 1
Back Extra
Summary 2	If \(a\) and \(m\) aren't relatively prime
Back Extra 2	Say \(a=4\) and \(m=6\), no matter what you multiply \(4\) by, it can only be \(\equiv 0,2,4\pmod 6\) which are increments of \(2\) since \(\gcd (4,6)=2\)
Summary 3	Using the inverse
Back Extra 3	Knowing the inverse of \(a\) modulo \(m\), then we can solve\(ax \equiv b \pmod m\)\(\overline a ax \equiv \overline a b \pmod m\)\(x \equiv \overline a b \pmod m\)because by definition, \(\overline a a \equiv 1 \pmod 1\)
Summary 4
Back Extra 4
Summary 5
Back Extra 5
Summary 6
Back Extra 6
Summary 7
Back Extra 7
Summary 8
Back Extra 8
Summary 9
Back Extra 9
Summary 10
Back Extra 10

Text	The generalized pigeonhole principle says thatif {{c1::\(N\) objects are placed into \(k\) boxes::what occurs}},then {{c2::there is at least one box containing \(\geq\Large\lceil{\frac Nk}\rceil\) objects::conclusion}}.
Replace
Answer
Attached
Overlapping
Subject Clozes
Deck ID	857020437
Summary 1
Back Extra	\(\lceil x \rceil\) is the ceiling function, which rounds \(x\) up to the next greater integer.
Summary 2
Back Extra 2
Summary 3
Back Extra 3
Summary 4
Back Extra 4
Summary 5
Back Extra 5
Summary 6
Back Extra 6
Summary 7
Back Extra 7
Summary 8
Back Extra 8
Summary 9
Back Extra 9
Summary 10
Back Extra 10

🍒 MATH 213 Basic Discrete Math

====================================================

⭐️ Features ⭐️:

📖 Contents of the deck, organized by tags 📖:

❤️ Support 😊:

Sample Data