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SD.College, Alappuzha Department of Mathematics Course Outcomes |
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B.Sc Mathematics |
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| Semester I | Methods of Mathematics | MM 1141 | In this paper, we quickly review the fundamental methods of solving problems viz. The limiting method, finding the rate of changes through differentiation method, and finding the area under a curve through the integration method. | |
| Semester II | Foundations of Mathematics | MM 1221 | The rigorous study of mathematics begins with understanding the concepts of sets and functions. After that, one needs to understand the way in which a mathematician formally makes statements and proves or disproves it. We start this course with an introduction to these fundamental concepts. Apart from that, the basic of vector calculus is to be revised
before moving to more advanced topics |
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| Semester III | Elementary Number Theory and Calculus – I | Code: MM 1341 | Towards beginning the study on abstract algebraic structures, this course introduces the fundamental facts in elementary number theory. Apart from that, calculus of vector valued functions and multiple integrals is also discussed. | |
| Semester IV | Elementary Number Theory and Calculus – II | Code: MM 1441 | As in the previous semester, towards beginning the study on abstract algebraic structures, this course introduces the fundamental facts in elementary number theory. Apart from that, calculus of vector valued functions and multiple integrals is also discussed. | |
| Semester V | Real Analysis – I | Code: MM 1541 | In this course, we discuss the notion of real numbers, the ideas of sequence of real numbers and the concept of infinite summation in a formal manner. Many of the topics discussed in the first two modules of this course were introduced somewhat informallyin earlier courses, but in this course, the emphasis is on mathematical rigor. A minimal introduction to the metric space structure of R is also included so as to serve as a stepping stone into the idea of abstract topological spaces. | |
| Semester V | Complex Analysis – I | Code: MM 1542 | Here we go through the basic complex function theory. | |
| Semester V | Abstract Algebra – Group Theory | Code: MM 1543 | The aim of this course is to provide a very strong foundation in the theory of groups.All the concepts appearing in the course are to be supported by numerous examples mainly from the references provided. | |
| Semester V | Differential Equations | Code: MM 1544 | In this course, we discuss how differential equations arise in various physical problems and consider some methods to solve first order differential equations and second order linear equations. For introducing the concepts, text [1] may be used, and for strengthening the theoretical aspects, reference [1] may be used. | |
| Semester V | Mathematics Software – LATEX & SageMath | Code: MM 1545 | Here we introduce two software which are commonly used by people working in Mathematics – a science typesetting software LATEX, and a mathematical computation and visualization software SageMath. The aim of introducing LATEX software is to enable students to typeset the project report which is a compulsory requirement for finishing their undergraduate mathematics programme succesfully. The aim of learning SageMath is to
enable students to see how the computational techniques they have learned in the previous semesters can be put into action with the help of software so as to reduce human effort. Also, they should be able to use this software for further computations in their own in the forthcoming semester. |
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| Semester VI | Real Analysis – II | Code: MM 1641 | In the second part of the Real Analysis course, we focus on functions on R, their continuity, existence of derivatives, and integrability. | |
| Semester VI | Complex Analysis – II | Code: MM 1642 | Here we study contour integration methods,residue theory and evaluation of difficult real integrals using complex integration | |
| Semester VI | Abstract Algebra – Ring Theory | Code: MM 1643 | After discussing the theory of groups thoroughly in the previous semester, we move towards the next higher algebraic structure rings. As in the last semester, all the new concepts appearing in the course is to be supported by numerous examples mainly from the references provided. | |
| Semester VI | Linear Algebra | Code: MM 1644 | The main focus of this course is to introduce linear algebra and methods in it for solving practical problems. | |
| Semester VI | Integral Transforms | Code: MM 1645 | After completing courses in ordinary differential equations and basic integral calculus, we see here some of its applications | |
| Semester VI | Graph Theory (Elective) | Code: MM 1661.1 | Overview of the Course: The course has been designed to build an awareness of some of the fundamental concepts in Graph Theory and to develop better understanding of the subject so as to use these ideas skillfully in solving real world problems. |