Department of Mathematics, PMCOE Govt. Tulsi College, Anuppur (M. P.) 484224

Programme OutcomesB.Sc.(Mathematics)

Programme Outcomes: After completing B.Sc.Mathematics, students will be able to appear in master degree programsin any professional or regular subjects. On successful completion ofB.Sc. Mathematics course as per NEP-2020, students can get directadmission in research degree (Ph.D.). B.Sc. Mathematics graduatestudent can successfully contribute in civil services by appearing instate P.S.C. and U.P.S.C. exams. By appearing in Bank, Railway, S.S.C.and other administrative exams, student can make their future bright.B.Sc. Mathematics graduate student can get fame in the country andabroad in academic and research work by getting admission throughentrance examination in different Institutes of repute like IITs, IISc,NITs, Indian Statical Institutions, Indian Institute of Science Educationand Research, National Institute of Science Education and Research,HRI, Central and State Universities.

Analyze whether afinite set of vectors in a vector space is linearly independent. Explain theconcepts of basis and dimension of a vector space. Understand the lineartransformations, rank and nullity, matrix of a linear transformation, algebraof transformations and change of basis. Compute the characteristic polynomial,eigenvalues, eigenvectors, and eigenspaces, as well as the geometric and the algebraicmultiplicities of an eigenvalueand apply the basic diagonalization result.

The course of B.Sc. second year Major II /Minor/Open Elective will enable thestudents to:

         Understand many properties of the real line R and sequences.Calculate the limit superior, the limit inferior, and the limit of a bounded sequence.  Apply the mean value theorems and Taylor's theorem. Apply the various tests to determine convergence and absoluteconvergence of an infinite series of real numbers.

Formulate, classifyand transform partialdifferential equations into canonical form.

The course of B.Sc. third year in Major first paper will enable the students to:    

                Understand numerical methods to find the solution of a system of linearequations. Compute interpolation value for real data. Find quadrature by usingvarious numerical methods. Solve system of linear equations by using variousnumerical techniques. Obtain solutions of ordinary differential equations byusing numerical methods.

The course of B.Sc. third year in Major second paper will enable the students to:

            Apply the Boolean algebra,switching circuits and their applications. Minimize the Boolean Function usingKarnaugh Map. Understand the lattices and their types Graphs, their types andits applications in study of shortest path algorithms. Test whether two givengraphs are isomorphic. 6. Understand the Eulerian and Hamiltonian graphs.Represent graphs using adjacency and incidence matrices.

The course of B.Sc. third year in Minor  / Open Elective paper will enable the students to:   

Using the Booleanalgebra in logical problems. Minimize the Boolean Function using Karnaugh Map.Understanding the various logic gates. Applying the circuits in logicalproblems.

The course of B.Sc.  Fourth year in First paper will enable the students to:

Understand the basic concepts of group operationsand their applications. Apply the Sylow's theorem to characterize certainfinite groups. Know the fundamental concepts in ring theory theory such as. polynomialrings, Euclidean domain and unique factorization domain. Learn the fundamentalproperties of finite field extensions and classification of finite fields.Analyzing the characterize perfect fields using separable extensions. Constructexamples of automorphism group of a field and Galois extensions.

Thecourse of B.Sc.  Fourth year in second paperwill enable the students to

 Learn theproperties of Riemann and Riemann-Stieltjes integrable functions andapplications of the fundamental theorems of integration. Understand theconcepts of convergence and term by term integration and differentiation of apower series. Understanding and evaluating uniform convergence of series ofreal valued functions. Analyzing the relation between uniform convergence andcontinuity, uniform continuity and differentiation and integration of sequencesof real valued functions. Determine interior, closure, boundary and limitpoints of metric space.

Thecourse of B.Sc.  Fourth year in Thirdpaper will enable the students to

Determine interior, closure, boundary, limit points,basis and subbasis of topological spaces. Check whether a collection of subsetsis a basis for a given topological space or not and determine the topology generatedby a given basis. Identify the continuous maps between two spaces and maps froma space into product space. Determine common topological properties of giventwo spaces. Recognize Hausdorff spaces, Tychonoff spaces and normal spaces andunderstand first and second countable spaces and separable spaces.

Thecourse of B.Sc.  Fourth year in Fourthpaper will enable the students to

Visualize complex numbers as points of R² andstereographic projection of complex plane on the Riemann sphere. Recognize thesignificance of differentiability and analyticity of complex functions. UseCauchy-Goursat theorem and Cauchy integral formula in evaluation of contourintegrals. Apply Liouville's theorem in fundamental theorem of Algebra. LearnTaylor and Laurent series expansions of analytic functions. Classify the natureof singularity, poles and residues and apply Cauchy residue theorem.