Module Catalogues, Xi'an Jiaotong-Liverpool University   
 
Module Code: MTH105
Module Title: Mathematical Reasoning Logic and Problem Solving
Module Level: Level 1
Module Credits: 5.00
Academic Year: 2018/19
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: N/A
   
Aims
-To bridge the gap in language and philosophy between A-level (Gau-k Chinese equivalent) and University mathematics.

-To train students to think clearly and logically, and to appreciate the nature of definitions, theorems and proofs

-To help students develop a systematic approach to problem-solving

-To develop students’ skills to write proofs

-To acquaint the students with the Foundation of Mathematics
Learning outcomes 
On successful completion of this module, students are expected

A. To be able to analyze and solve simple problems.

B. To be able to develop alternative strategies when facing with a lack of progress.

C. To be able to make wider use of basic mathematics.

D. To be able to organize and present their arguments clearly and logically.

E. To have a basic understanding of the foundations of logic, set theory and discrete mathematics.
Method of teaching and learning 
Students will be expected to attend formal lectures and supervised tutorials in a typical week.
Syllabus 
Mathematical language and symbols. Definitions.

Theorems: hypothesis and conclusion, converse and contrapositive.

Proofs: direct proof and proof by contradiction; examples and counterexamples.

The language of set theory.

Relations. Functions, injection, surjections and bijections.

Introduction to Logic. Propositional Logic. Truth tables. Conjunction, disjunction, negation, implication, equivalence. Free and bound variables. Quantifiers, negation. Conjunction Normal Form and Disjunction Normal Form.

Proofs by Induction. Strong Induction.

Pigeonhole Principle.

Elementary counting techniques. Equivalence relations and Partitions. Partial Order Relations and Partially Ordered Sets.

Arithmetic modulo m. Recurrence Relations. Fibonacci Numbers.

Introduction to Graph Theory. First theorem of Graph Theory. Paths, walks and trails. Degree and degree sequences. Eulerian and Hamiltonian Graphs. Distance and Diameter. Connectivity.

Isomorphism. Trees. Prim’s algorithm. Kruskal’s algorithm. Directed graphs. Travelling Salesman Problem.
Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester 39     13      98  150 

Assessment

Sequence Method % of Final Mark
1 Formal Exam 90.00
2 Midterm 10.00

Module Catalogue generated from SITS CUT-OFF: 12/9/2019 11:24:59 PM