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Main
UQU Programs
Mathematics

Number Theory

MTH3205
4 hours English

Number Theory

Number Theory
MTH1201 Foundation of Mathematics
4 hours No requisites
1 Revision on prime numbers and basic properties of them, multiplicative function and Diophantine equation
2 Divisibility, Greatest Common Divisor GCD
3 Least Common Multiple LCM and Euclidean Algorithm
4 Writing the GCD as a Linear Combination and / Fundamental Theorem of Arithmetic, FTA
5 Definition and Basic Properties of Congruence and Least Residue
6 Linear Congruences, Euler-Fermat Theorem and Wilson’ s Theorem
7 Chinese Remainder Theorem, C.R.T
8 Arithmetical Functions with some examples
9 Multiplicative and Completely Multiplicative Functions
10 Perfect, Deficient, Abundant, Mersenne, and Fermat Numbers
11 Quadratic Residues and Quadratic Non-Residues and / Legendre’s Symbol
12 Quadratic Reciprocity Law and order of an integer
13 Primitive Root and Continued Fractions
14 Diophantine Equation
15 Others: Revision and activities, Exam, quizzes
1.1 Mapped to: K1

Understand the prime numbers and their properties.

Teaching Strategy Lecture
Assessment Methods Exams quizzes
1.2 Mapped to: K2

Define the concepts of divisibility, congruence, greatest common divisor, least common multiple, and primitive root.

Teaching Strategy Lecture
Assessment Methods Exams quizzes
2.1 Mapped to: S1

Find the GCD of two natural numbers by using Euclidean Algorithm and write it as a linear combination.

Teaching Strategy Lecture
Assessment Methods Exams quizzes
2.2 Mapped to: S2

Solve systems of linear congruences by using Chinese Remainder Theorem.

Teaching Strategy Lecture
Assessment Methods Exams quizzes
2.3 Mapped to: S5

Be able to prove if an arithmetic function is a multiplicative or completely multiplicative function.

Teaching Strategy Lecture
Assessment Methods Exams quizzes
2.4 Mapped to: S6

Solve linear Diophantine equation of two variables and be able to write a number as a continued fraction.

Teaching Strategy Lecture
Assessment Methods Exams quizzes
3.1 Mapped to: V1

Adhere to self-management, self-learning and think in a critical manner.

Teaching Strategy Lecture
Assessment Methods Exams quizzes
3.2 Mapped to: V2

Work effectively in groups, manage time, collaborate and communicate with others positively and ethically.

Teaching Strategy Lecture
Assessment Methods Exams quizzes
Assessment
Weight
Midterm exam
30%
Homework and assignments
20%
Final Exam
50%
Total
100%