| CODE | MAT1212 | ||||||||||||
| TITLE | Introductory Analysis | ||||||||||||
| UM LEVEL | 01 - Year 1 in Modular Undergraduate Course | ||||||||||||
| MQF LEVEL | 5 | ||||||||||||
| ECTS CREDITS | 6 | ||||||||||||
| DEPARTMENT | Mathematics | ||||||||||||
| DESCRIPTION | - Natural numbers and the principle of induction. - Logic, methods of proof. - The Real number line: - The completeness axiom, - The Archimedean property of the real numbers, - 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. - Sequences of real numbers: - Convergence, - Tests of convergence. - Series: - Conditional and absolute convergence, - Tests for convergence. Study-Unit Aims: The aim of this study-unit is to introduce students to the language of mathematics, including logic, sets, and functions, as well as the integers and real numbers. Students will also be introduced to techniques for constructing mathematical statements and proofs, developing the skills to be able to read and write advanced mathematics. The second part of the study-unit considers sequences and series of real numbers, how to determine if they converge, and if so, to what limit. 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; - Analyse basic definitions and results about sets and functions; - Use a variety of proof techniques to investigate the above topics; - Work with sequences and series; - Distinguish between different rates of convergence. 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; - Write rigorous mathematical statements; - Investigate the basic properties of integers and real numbers; - Use convergence tests to determine whether sequences and series converge; - Find limits of sequences and series. Main Text/s and any supplementary readings: Main Texts: - Abbott S. (2001), Understanding Analysis, Springer. (Available at the Library.) - Bartle R. & Sherbert D.(1999), Introduction to Real Analysis. Wiley, 3rd edition. Supplementary Readings: - Daepp, U. & Gorkin, P. (2011), Reading, Writing and Proving: A Closer Look at Mathematics. Springer, 2nd edition. (Available at the Library.) (Available at the Library.) - Ross K. (2013), Elementary Analysis: The Theory of Calculus. Springer, 2nd edition. (Available at the Library.) |
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| ADDITIONAL NOTES | Pre-requisite Qualifications: Advanced Level Pure Mathematics | ||||||||||||
| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Pierre Sandre Farrugia Joseph Muscat (Co-ord.) |
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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 2024/5. It may be subject to change in subsequent years. |
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