Faculty                                 : Mathematics and Natural Science Study Program                              : International Mathematics Education Course/Code                       : Number Theory / MAA 209
Credit                                 : Teory = 2 (two) SKS, Practise = - ( - ) SKS Semester                             : 2 (two)
Prerequisite/Code                : Logic and Set, MAA301
Professor                             : Nikenasih Binatari, M.Si 

I. Course Description

Number theory is one of the oldest and most beautiful branches of Mathematics. It abounds in problems that yet simple to state, are very hard to solve. In this course, we will discuss about number, particularly integer, and it properties. First of all, we cover some preliminary tools we need such as well ordering, mathematical induction, and pigeon hole principle. Next, we will study about divisibility, congruence, unique factorization, gcd and lcm, fundamental theorem of arithmetic, linear diophantine equation and arithmetic functions.

II. Standard of Competence

Upon completing this course, students should be able to understand the properties of integer and then apply the properties to solve some integer problems.

III. Activity Plan

Meeting
Basic Competence
Essential Concept
Learning
Strategies
Referencee
Character



1,II


Students should understand the preliminary tools needed to study number theory

Preliminaries
-     Introduction
-     Well Ordering
-     Mathematical Induction
-     Pigeon Hole Principle


Lecturing and
Exercises



A,B


Curiousity, reasonable Understand


III,IV

Students should be able to determine wether a number is divisbile by other or not

Divisibility
-     Divisibility
-     Division Algorithm

Lecturing, Discussion and Exersices


A, B


Understand, creative


V,VI

Students should be able to determine the remainder of a number if it’s divided by other

Congruences
-     Congruences
-     Complete residues

Lecturing, Discussion and Exersices


A, C


Creative




VII,VIII,IX

Students should be able to find the gcd and lcm of two numbers, to determine wether a number is prime or not, then to determine
the number of factor, sum of factor
of a number.

Unique Factorization
-     GCD and LCM
-     Primes
-     Fundamental Theorem of
Arithmetic
-     Arithmetic Functions



Lecturing, Discussion and Exersices




A, B




Creative

X

Midterm Exam



XI,XII

Students should be able to find the gcd of two number using euclidean algorithm, to solve linear diophantine equation and to solve linear congruences


Linear Diophantine Equation
-     Euclidean Algorithm
-     Linear Congruences


Lecturing, Discussion and Exersices



A, C



Creative


XIII,XIV,XV

Students should be able to understand some theorem about integer

More of congruences
-     Fermat Little’s Theorem
-     Wilson’s Theorem
-     Euler’s Theorem

Lecturing, Discussion and Exersices


A, C


Creative

XVI

Final Exam

IV. Reference

Compulsory :
[A]   Lecturer Notes. David A. Santos. Number Theory for Mathematical Contests. 2005.

Additional :
[B]   Sukirman. 2006. Pengantar Teori Bilangan. Yogyakarta : Hanggar Kreator.
[C]  Ore Oystein. 1948. Number Theory and Its History. First Edition. USA : McGraw-Hill Book Company, Inc.


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