Brief Information

• Name : Finite Mathematics 유한수학
• Lecturer : Sang-Mok Kim?김상목
• Semester : 2016 Spring
• Major?: BS, Mathematics
• Textbook
  • 박승안 (2012) 『이산수학』. 3판. 경문사
• Syllabus 😕Syllabus_2016-5-1__Finite Mathematics.pdf
• In?short
  • The professor said this course is about discrete mathematics.

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Assignments

• [Assignment 1] Logic and Functions | Finite Mathematics
  • Finite Mathematics) Assignment 1) Logic and Functions.pdf
• [Assignment 2] Functions, Mathematical Induction, Equivalence Relations, and?Selected Exercises in Chapter 1 of the Textbook | Finite Mathematics
  • Exercises of assignment 2: Finite Mathematics) Assignment 2.pdf
  • Solution:
• [Assignment 3] Sets, Functions, the Pigeonhole Principle and the Binomial Theorem
  • Finite Mathematics) Assignment 3.pdf
• [Assignment 4]?Linear Recurrence Relations including the Tower of Hanoi Sequence, the Catalan Number, and the Fibonacci Sequence
  • Deriving the General Form of the Tower of Hanoi Sequence
  • Finite Mathematics) Assignment 4) What is the Catalan number and its Examples.pdf
  • Finite Mathematics) Assignment 4) Solve Linear Recurrence Relations and the Fibonacci Sequence.pdf
• [Assignment 5]
  • Finite Mathematics) Assignment 5) Prove Some Recurrence Relations and Solve a Sequence Using Generating Functions.pdf

Lectures

1. Introduction | 2016-03-07 Mon.

• In South Korea, mathematics graduates are demanded in lots of industries. However, there are few people good at mathematics and English literacy.
• If you learn English through mathematics, you can get used to using advanced English words.
• The revolution of the ‘fundamental theorem of calculus’.
• Continuity makes us use the Intermediate Value Theorem(IVT), which can be used to find approximate values.
• Following the?uncertainty principle, the observing the nature has limit. Between some boundaries, it is still reasonable to consider the value we found as the limit of the solution.

Classification of mathematics

• By approach: algebra, analysis
• By theme: number theory, topology, geometry, combinatorics

Story Flow of Analysis

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2.?Finite and Infinite?| 2016-03-09 Wed.

• Number
• The category of the numbers
• What is infinity?
• Infinity sets
• |\mathbb{N}|=|\mathbb{Q}|=\aleph_{0}<|\mathbb{R}|=\aleph_{1}
• Whether \aleph_{1/2} exists or not, the foundation of mathematics is not affected.
• Know how to prove?|\mathbb{N}| < |\mathbb{R}|
• “We live in the DISCRETE world.” “우리는 유한의 세계에 살고 있다.”
• “There are an infinity-like finite set.” “무한 같은 유한이 있다.”