Study-Unit Description

Study-Unit Description


CODE MAT1100

 
TITLE Introductory Mathematics

 
UM LEVEL 01 - Year 1 in Modular Undergraduate Course

 
MQF LEVEL 5

 
ECTS CREDITS 4

 
DEPARTMENT Mathematics

 
DESCRIPTION - Natural numbers and the principle of induction.
- Integers:
    - Divisibility,
    - Prime numbers,
    - The greatest common divisor and the Euclidean algorithm,
    - The fundamental theorem of arithmetic;
- Rational and real numbers:
    - The completeness axiom,
    - The Archimedean property of the real numbers,
    - Inequalities.
- Sets:
    - Inclusion, union, intersection,
    - De Morgan’s laws;
- Ordered pairs and the Cartesian product of sets;
- Functions:
    - The function as a mapping,
    - Injectivity and surjectivity,
    - Composition of functions,
    - Inverse functions.

Study-unit Aims:

The aim of this study-unit is to introduce the students to basic notions of advanced mathematics such as sets and functions, as well as the integers and real numbers. Students will also be introduced to techniques for constructing proofs, and will be given ample opportunity to practice these skills. This study-unit is a fundamental prerequisite to the rest of the undergraduate Mathematics programme, in particular the study units in Analysis and Algebra from the second semester onwards.

Learning Outcomes:

1. Knowledge & Understanding:

By the end of the study-unit the student will be able to:
- Describe the basic properties of integers and real numbers, and prove fundamental theorems about them.
- Analyse basic definitions and results about sets and functions.
- Use a variety of proof techniques to investigate the above topics, in preparation for the more advanced work to be done in subsequent semesters.

2. Skills:

By the end of the study-unit the student will be able to:
- Use the definitions and properties of set structures and functions to prove results about these mathematical objects.
- Investigate the basic properties of integers and real numbers.
- Construct proofs by induction in a variety of contexts.

Main Text/s and any supplementary readings:

Main Texts:

- Daepp, U. and Gorkin, P., Reading, Writing, and Proving: A Closer Look at Mathematics, Springer, 2nd Edition, 2011.

Supplementary Readings:

- D’Angelo J.P. and West D.B., Mathematical Thinking: Problem-Solving and Proofs, Prentice Hall, 2nd Edition, 2000.
- Schumacher C., Chapter Zero: Fundamental Notions of Abstract Mathematics, Addison-Wesley, 2nd Edition, 2000.
- Devlin K.J., Sets, Functions and Logic, Chapman and Hall, 3rd Edition, 2003.
- Epp S., Discrete Mathematics with Applications, Brooks Cole, 4th Edition, 2010.

 
ADDITIONAL NOTES Pre-requisite Qualifications: Advanced Level Pure Mathematics

 
STUDY-UNIT TYPE Lecture and Independent Study

 
METHOD OF ASSESSMENT
Assessment Component/s Assessment Due Sept. Asst Session Weighting
Examination (2 Hours) SEM1 Yes 100%

 
LECTURER/S John B. Gauci

 

 
The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the description above applies to study-units available during the academic year 2023/4. It may be subject to change in subsequent years.

https://www.um.edu.mt/course/studyunit