### Department of Mathematics

Course Outcomes, Program Outcomes and Program Specific Outcomes

Course Offered: 2014 Onwards

### BSc Mathematics

 Sem Course code & Course Title Course Outcome I MM 1141 Methods of Mathematics Explain Theory of Numbers and its application to cryptography. Understand the basis of Functions and their graphs, concept of limits, continuity and differentials. Impart knowledge of Conic sections and sketching of conics. II MM 1221 Foundations of Mathematics Explain Foundations of Algebra . Provide knowledge in Foundations of Calculus and Analytic geometry. Polar coordinates in coordinate geometry. III MM 1341 Algebra and Calculus-I Create awareness in Basic concepts of Abstract Algebra. Develop deeper understanding of Vectors in three dimensional space. Familiar with Calculus of vector valued functions. IV MM 1441 Algebra and Calculus-II Provide knowledge of Polynomials and division theorem. Familiar with Calculus of functions of two or more variables, Surface area and volume of solids. Provide knowledge of Triple integral and using it to compute volume. V MM 1541 Real Analysis-I MM 1542 Complex Analysis I MM 1543 Differential Equations MM 1544 Vector Analysis MM 1545 Abstract Algebra I MM 1551 Open Course Project MM 1541 Real Analysis-I Familiar with Applications of completeness property. Familiar with Basic idea of mathematical analysis. MM 1542 Complex Analysis I Explain Properties of differentiable complex functions of open sets. Realise Harmonic functions .Familiar with Concepts of conformal mapping MM1543:- Differential equations and their applications. Explain Applications of Differential equations to physics, chemistry and biology.  Familiar with Differential equations with constant coefficients and their solutions. Familiar with Second order equations with variable coefficients and their solutions. Understand the basis of Laplace transform. MM1544 :- Vector Analysis Understand the basis of Vector fields, graphical representation, line integrals. Explain Green’s Theorem and its applications MM 1545 Abstract Algebra I Detailed study on Isomorphisms of binary structures Discussed about cosets and Lagrange’s Theorem . Also explained direct products of groups MM 1551.2 Open Course (Business Mathematics) Discussed about  compound interest, present value, interest and discount, nominal rate of discount, effective rate of discount, force of discount, Depreciation. Basic ideas about differentiation and integration with its applications Explain types of index numbers, methods of construction of price index numbers, Laspeyer’s price index number, Paasche’s price index. Components of time series, Measurement of Trend VI MM 1641 Real Analysis-II MM 1642 Linear Algebra MM 1643 Complex Analysis II MM 1644 Abstract Algebra II MM 1645 Computer Programming (Pract.) MM 1661.1 Elective Course MM 1646 Project MM 1641 Real Analysis-II Develop deeper understanding of Real - valued functions, properties of continuity ,differentiability and Riemann integral.  Establish the links between anti-differentiation and Riemann integrals. MM 1642 Linear Algebra Provide knowledge in Algebra of matrices and some applications of matrices to conic sections and system of linear equations . Familiar with Invertible matrix and linear mappings Describe Matrix connection. MM 1643 Complex Analysis II Discussed  how the coefficients of the series are related to the derivatives of the function, isolated singular points and residues .Explain application of the Residue Theorem,  Application of Contour Integral Methods to Evaluation and Estimation of Sums. MM 1644 Abstract Algebra II Discuss homomorphism of groups and factor groups Discuss homomorphisms and factor rings. MM 1645 Computer Programming (Pract.) Impart knowledge inLatex Programming Familiar with Python MM 1661.1 Elective Course (Graph Theory) Explain History of graph theory.  Create awareness in history of graph theory. Realise Basic concepts of graphs. Desribe Applications.

### Complementary in Mathematics BSc Physics

 Sem Course code & Course Title Course Outcome I MM 1131.1 Differentiation and Analytic Geometry Describes some applications of mathematical methods to physics. Give basic ideas about functions and it graphs with examples from physics  Explains about different types of functions and their properties. Also give an idea about differentiation with applications to physics. II MM 1231.1 Integration and Vectors Give details about applications of integral calculus to problems in physics. Explains vector calculus and its applications III MM 1331.1 Theory of Eqs., Differential Eqs., and Theory of Matrices Describes analytical methods for solving polynomial equations.  Give basic concepts about differential equations and their solutions. IV MM 1431.1 Complex Analysis, Fourier Series and Transforms Explains basic concepts about complex numbers. Introduce the idea of complex integration and differentiation.

### Complementary in Mathematics BSc Chemistry

 Sem Course code & Course Title Course Outcome I MM1131.2  Differentiation and matrices Create awareness on differentiation with application to chemistry.  Impart knowledge on basicconcepts of matrices II MM1231.2 Integration, Differential equations and Analytic geometry Create awareness on integration with application to chemistry. Equip students to familiarize with the basic concepts about differential equations and their solutions. III MM1331.2 Theory of equations and vector analysis Describes applications of fundamental theorem to equations.  Convey an idea of vector differentiation and integration IV MM1431.2  Abstract Algebra, linear transformations and coordinate systems Abstract Algebra, linear transformations and coordinate systems Enable the students to achieve the concept of Groups, Rings and Vectorspaces..

### Complementary in Mathematics BSc Geology

 Sem Course code & Course Title Course Outcome I MM 1131.3  Differentiation and Theory of Equations The graph showing direct and inverse proportional variation,  Parametric equations. Cycloid Techniques of differentiation. Higher derivatives. Implicit differentiation. Relatedrates.Local linear approximation Basics of limit, Infinite limits and verticalasymptotes. Limits at infinity and horizontal asymptotes. Local maxima and minima of functions of two variables. Use of partial derivatives inlocating local maxima and minima. Lagrange method for finding maximum/minimumvalues of functions subject to one constraint. II MM 1231.3  Integration, Differential  Eqs. and Matrices Find volume using integration Second order linear homogeneous ODEs with constant coefficients. The characteristicequation and its use in finding the general solution. Extension of the results to higherorder ODEs. III MM 1331.3  Analytic Geometry, Complex Nos. and Abstract Algebra Conic sections in polar coordinates. Eccentricity of an ellipse as a measure of flatness. Polar equations of conics. Groups, rings and Vector space IV MM 1431.3  Vector Analysis and Fourier Series Gradient as an operator and its properties.Directional derivative of a scalar field and its significance. Use of gradient vector incomputing directional derivative. Vector integration Fourier integral and transforms

### PROGRAMME OUTCOME

1.  Mathematics is a powerful tool with many applications, so in this programme students could acquire basic and deep knowledge in various branches of Mathematics.
2. The resources gives sensible thinking, problem- solving capabilities and thecapability to think in subjective ways.
3.  Provides an effective communication skill.
4. Provides knowledge in python and latex thoroughly.

### PROGRAMME SPECIFIC OUTCOME

1. The degree programme will provide both mathematical knowledge and communication skills.
2. Applied Mathematics can lead to many career opportunities.
3. Mathematics is a building block for everything in our dailylives including mobile devices, architecture,money,in sports etc.

Course Offered:  2018 Onwards

### BSc Mathematics

 Sem Course code & Course Title Course Outcome I MM 1141 Methods of Mathematics Understand the basis of Functions and their graphs, concept of limits, continuity and differentials. Impart knowledge of integration Finding area between two curves, volumes of some three dimensional solids, length of a plane curve, surface of revolution and its area. II MM 1221 Foundations of Mathematics Explain Foundations of Logic and Proof. Provide knowledge in Sets, Relations and Functions Foundations of Polar coordinates in coordinate geometry and vector calculus. III MM 1341 Elementary Number Theory and Calculus - I Create awareness in Basic concepts of elementary number theory. Develop deeper understanding of Vectors in three dimensional space. Familiar with Calculus of vector valued functions. Familiar with Calculus of. functions of two or more variables, Surface area and volume of solids IV MM 1441 Elementary Number Theory and Calculus II Provide knowledge of  divisibility-numbers Discuss Linear system of congruence equations, Chinese Remainder Theorem and some applications Provide knowledge of Triple integral and using it to compute volume. Familiar with Calculus of vector differentiation and integration V MM 1541 Real Analysis-I MM 1542 Complex Analysis I MM 1543 Abstract Algebra - Group Theory MM 1544 Differential Equations MM 1545Mathematics Software - LATEX &SageMath (Pract.) MM 1551.2 Open Course Project MM 1541 Real Analysis-I Familiar with Applications of completeness property. Familiar with Basic idea of mathematical analysis. MM 1542 Complex Analysis I Explain Complex numbers and Analytic Functions differentiable complex functions of open sets. Realise Elementory functions .Familiar with Concepts of complex integration MM1543:-Abstract Algebra - Group Theory Important features of cyclic groups and results onorder of elements Explain properties of permutation groups and isomorphism Discussed Langrange’s Theorem MM1544:- Differential equations Explain first order equations and various methods to solve Discuss second order equations and various methods to solve MM1545 :- Mathematics Software  LATEX &SageMath Impart knowledge inLatex Programming Familiar with SageMath MM 1551.2 Open Course (Business Mathematics) Discussed about  compound interest, present value, interest and discount, nominal rate of discount, effective rate of discount, force of discount, Depreciation. Basic ideas about differentiation and integration with its applications Explain types of index numbers, methods of construction of price index numbers, Laspeyer’s price index number, Paasche’s price index. Components of time series, Measurement of Trend VI MM 1641 Real Analysis-II MM 1642 Complex Analysis II MM 1643 Abstract Algebra – Ring Theory MM 1644 Linear Algebra MM 1645 Integral Transforms MM 1661.1 Elective Course (Graph Theory) MM 1646 Project MM 1641 Real Analysis-II Develop deeper understanding of Real - valued functions, properties of continuity, intermediate value theorem, Monotone functions and their continuity.  Establish the links between differentiability and continuity Explain Riemann integration MM 1642 Complex Analysis II Discussed  Series Representations for Analytic Functions : Sequences and Series, Taylor Series, PowerSeries, Mathematical Theory of Convergence, Laurent series, Zeros and Singularities, The point at Infinity Explain application of the Residue Theorem Discuss Conformal Mapping  MM 1643 Abstract Algebra –Ring Theory Discuss concept of rings, subrings and also explain how factor rings are defined using ideals Introducing the definition of ring homomorphisms and their properties Types and divisibility properties of integral domains. MM 1644 Linear Algebra Introducingthe geometrical intrepretation of linear equations linear transformations and their properties are to be discussed. Types of transformations like rotations,projections, reflections are to be considered . MM 1645 Integral Transforms Familiar with Laplace Transform Impart knowledge in Fourier Series MM 1661.1 Elective Course (Graph Theory) Explain basicsof graph theory.  Create awareness in Euler Tours and Hamiltonian Cycles

### Complementary in Mathematics BSc Physics

 Sem Course code & Course Title Course Outcome I MM 1131.1 Calculus with applications in Physics I Describetheorems of differentiation -Rolles', Mean Value Theorems. Give basic ideas definite and improper integral  Explains about infinite series and limits Also give anidea about vector algebra II MM 1231.1  Calculus with applications in Physics II Explains basic concepts about complex numbers Give details total differential and total derivative Give details about applications of multiple integral Explains vector differentiation III MM 1331.1  Calculus and Linear Algebra Describes ordinary differentiation  Give basic concepts about vector integration Explain Fourier Series Basic Linear algebra and matrices IV MM 1431.1  Complex Analysis, Special Functions and Probability Theory Detailed study of Complex analysis. Introduce the idea of special function .Basics of Probability and Statistics

### Complementary in Mathematics BSc Chemistry

 Sem Course code & Course Title Course Outcome I MM1131.2  Calculus with applications in Chemistry I Describe theorems of differentiation -Rolles', Mean Value Theorems Introduce Complex numbers  Impart knowledge in vector algebra Basic integration with applications to Chemistry II MM1231.2 Calculus with applications in Chemistry II Give details total differential and total derivative Discuss about Infinite Series and limits. Create awareness on vector differentiation Give details about applications of multiple integral III MM1331.2 Linear Algebra, Probablity Theory & Numerical Methods Basic Linear Algebra Describeprobability and Statistics Convey some ideas of numerical methods IV MM1431.2  Differential Equations, Vector Calculus and Abstract Algebra Explain Ordinary Differential Equations Discuss Vector Integration - Line, surface and volume integrals Introduce linear algebra

### Complementary in Mathematics BSc Geology

 Sem Course code & Course Title Course Outcome I MM 1131.3  Algebra, Geometry and Trigonometry Preliminary algebra Geometry : lines and angles, triangles, quadrilaterals, circles, measurement of irregular areas, solid geometric figures; plane analytic geometry Basic Trignometry II MM 1231.3  Calculus and Linear Algebra Introduce Exponential and logarithmic functions. Discuss basic linear algebra Sequence and Series Concept of differentiation and Matrices III MM 1331.3  Complex Numbers, Algebra and Calculus Basics of complex numbers Solving equations and inequalities Discuss about integration Expanding functions in series IV MM 1431.3  Basic Statisticsand Differential Equations Introduce statistics Discuss methods of fitting curves Describe methods of solving differential equations

### PROGRAMME OUTCOME

1.  Mathematics is a powerful tool with many applications, so in this programme students could acquire basic and deep knowledge in various branches of Mathematics.
2. The resources gives sensible thinking, problem- solving capabilities and the capability to think in subjective ways.
3. Provides an effective communication skill.
4. Provides knowledge in SageMath and latex thoroughly.