B.Sc. in Statistics (STM364T)
Course Outcomes CO COGNITIVE ABILITIES COURSE OUTCOMES CO1 REMEMBERING Recall fundamental concepts of quality control, control charts, and variation in industrial processes. CO2 UNDERSTANDING Explain the principles of Statistical Quality Control (SQC) and the theory behind control charts for variables and attributes. CO3 APPLYING Apply methods for constructing x̄, R, S, p, np, c, and u charts to monitor process quality. CO4 ANALYSING Analyse control charts to detect assignable causes of variation and interpret process behavior. CO5 EVALUATING Evaluate process control performance using tolerance limits, specification limits, and operating characteristic (OC) function. CO6 CREATING Design quality control procedures and select appropriate control charts for real-world industrial applications.
B. Sc. in Mathematics (MAMDC364P)
Course Outcomes CO COGNITIVE ABILITIES COURSE OUTCOMES CO1 REMEMBERING Recall and define the basic properties of graphs; identify and compute order, size, degree, and completeness of given graphs. CO2 UNDERSTANDING Explain and construct incidence and adjacency matrices; interpret walks, paths, and cycles to understand the structure of graphs. CO3 APPLYING Apply Breadth First Search (BFS), Backtracking, and Dijkstra’s Algorithm to determine the shortest paths between vertices in connected and weighted graphs. CO4 ANALYSING Analyze connectivity of graphs using adjacency matrices and the fusion algorithm; decompose graphs to identify components and relationships among vertices. CO5 EVALUATING Evaluate Euler circuits using Fleury’s algorithm; assess the correctness and optimality of minimal spanning trees obtained through Prim’s and Kruskal’s algorithms. CO6 CREATING Design and implement algorithms to model and solve real- world problems using graph representations; construct efficient graph-based solutions for network and optimization problems.
B. Sc. in Mathematics (MAM363P)
Course Outcomes CO COGNITIVE ABILITIES COURSE OUTCOMES CO1 REMEMBERING Recall and define the basic concepts of rings, commutative rings, rings with unity, and finite rings; construct their operation tables and verify ring axioms. CO2 UNDERSTANDING Explain and interpret the structures of ideals, integral domains, quotient rings, finite and extension fields, and distinguish between maximal and prime ideals. CO3 APPLYING Apply the Euclidean algorithm to find the GCD of two polynomials; test irreducibility and perform factorization; determine rational zeros over various fields. CO4 ANALYSING Analyze graph connectivity using adjacency matrices and fusion algorithms; determine shortest paths, minimum spanning trees, and Euler tours using Kruskal’s, Prim’s, Dijkstra’s, Breadth-First, Backtracking, and Fleury’s algorithms. CO5 EVALUATING Evaluate and test the properties of metric spaces, compactness, and connectedness; assess uniform convergence of sequences and series using appropriate theorems and convergence tests. CO6 CREATING Develop and construct new quotient rings, operation tables, and examples of finite fields and extension fields; design algorithms and proofs involving uniform convergence and power series.
B. Sc. in Mathematics (DSCCMAT362T)
Course Outcomes CO COGNITIVE ABILITIES COURSE OUTCOMES CO1 REMEMBERING Recall the fundamental definitions and properties of relations, groups, rings, fields, subgroups, and ideals. CO2 UNDERSTANDING Explain the basic concepts of algebraic structures and interpret theorems such as Lagrange’s, Euler’s, and Fermat’s in context. CO3 APPLYING Apply the properties of groups, rings, and fields to solve algebraic problems CO4 ANALYSING Examine subgroup, coset, and ideal structures and distinguish between different algebraic systems. CO5 EVALUATING Test algebraic properties using relevant theorems and validate structures. CO6 CREATING Construct new examples of groups, rings, subrings, quotient rings, and demonstrate homomorphisms and isomorphisms.
B. Sc. in Mathematics (DSCCMAT361T)
Course Outcomes CO COGNITIVE ABILITIES COURSE OUTCOMES CO1 REMEMBERING Recall definitions, standard results, and fundamental concepts related to Riemann integration, convergence of sequences and series, and power series. CO2 UNDERSTANDING Explain the concepts of Riemann integrability, improper integrals, convergence and divergence of series, and the meaning of absolute and conditional convergence. CO3 APPLYING Apply appropriate tests to determine convergence of sequences and series, evaluate Riemann and improper integrals, and obtain expansions of elementary functions using power series. CO4 ANALYSING Analyze the behavior of sequences, series, and power series using limit superior, limit inferior, and convergence criteria, and distinguish between different types of convergence. CO5 EVALUATING Assess the validity of convergence tests, integrability conditions, and series expansions, and justify conclusions using rigorous mathematical reasoning. CO6 CREATING Construct power series representations, Taylor and Maclaurin expansions, and develop approximations or simple differential equation solutions using series methods.
B. Sc. in Mathematics (MAE355P)
Course Outcomes CO COGNITIVE ABILITIES COURSE OUTCOMES CO1 REMEMBERING Recall and define the fundamental concepts of graph theory such as order, size, degree, completeness, and connectedness of graphs. CO2 UNDERSTANDING Explain the construction and interpretation of adjacency and incidence matrices, and identify walks, paths, and cycles in given graphs. CO3 APPLYING Apply algorithms such as Breadth First Search (BFS), Backtracking, and Dijkstra’s algorithm to find shortest paths in connected and weighted graphs. CO4 ANALYSING Analyze graph connectivity using adjacency matrices and fusion algorithms; differentiate between connected and disconnected graphs based on algorithmic results. CO5 EVALUATING Evaluate the correctness and efficiency of graph algorithms such as Prim’s, Kruskal’s, and Fleury’s, and determine minimal spanning trees or Euler tours. CO6 CREATING Design and implement new graph-based models or algorithms to solve real-world network and optimization problems, demonstrating innovation and critical thinking.
B. Sc. in Mathematics (MAE354T)
Course Outcomes CO COGNITIVE ABILITIES COURSE OUTCOMES CO1 REMEMBERING Students will be able to recall and define basic concepts such as convex sets, convex combinations, extreme CO2 UNDERSTANDING Students will be able to explain the formulation techniques of linear programming problems and interpret different types of LPP through examples. CO3 APPLYING Students will be able to apply the Simplex Method, Big-M (Penalty) Method, and Dual Simplex Method to obtain optimal solutions of linear programming problems. CO4 ANALYSING Students will be able to analyze primal and dual relationships, interpret solutions of dual problems, and examine project networks using PERT and CPM to identify critical paths and floats. CO5 EVALUATING Students will be able to evaluate strategies in two-person zero- sum games using maximin and minimax principles, dominance rules, and compare different solution methods. CO6 CREATING Students will be able to construct and solve complex game theory models (2×n and 3×3 games) and develop approximate solutions using iterative and advanced methods.
B. Sc. in Mathematics (MAM353P)
Course Outcomes CO COGNITIVE ABILITIES COURSE OUTCOMES CO1 REMEMBERING Recall and define the fundamental concepts of Linear Programming Problems (LPP); identify and formulate problems and express them in standard and canonical forms. CO2 UNDERSTANDING Explain and interpret the graphical method, simplex method, Big-M method, and the principle of duality with suitable examples. CO3 APPLYING Apply the dual simplex method, and solve transportation problems using NWCM, LCM, and VAM methods; determine optimal solutions for balanced transportation and assignment problems. CO4 ANALYSING Analyze and compare variations in transportation and assignment problems; decompose complex linear programming models into subproblems; interpret computational outcomes. CO5 EVALUATING Evaluate and test the convergence of sequences and infinite series; distinguish between countable and uncountable sets; verify properties involving absolute value and triangle inequality. CO6 CREATING Construct and derive Fourier series representations; develop analytic functions and their harmonic conjugates; find transformations under f(z)=1 / z and apply De Moivre’s theorem to complex problems.
B. Sc. in Mathematics (DSCCMAT352T)
Course Outcomes CO COGNITIVE ABILITIES COURSE OUTCOMES CO1 REMEMBERING Recall Vedic Mathematics sutras for algebraic multiplication, division, factorisation, HCF, and LCM, along with fundamental properties of complex numbers and elementary functions. CO2 UNDERSTANDING Explain concepts of complex numbers, exponential and trigonometric forms, convergence of sequences and series, and basic properties of analytic functions. CO3 APPLYING Apply Vedic Mathematics techniques to simplify algebraic computations and use complex number properties in problem solving. CO4 ANALYSING Examine mappings, Cauchy-Riemann equations, and harmonic functions to identify analyticity and differentiability. CO5 EVALUATING Evaluate transformations, roots, and functional behaviors in the complex plane to test conformality and angle preservation. CO6 CREATING Construct conformal mappings and apply transformations (linear, fractional, and w=1/z) to model regions in the complex plane.
B. Sc. in Mathematics (DSCCMAT351T)
Course Outcomes CO COGNITIVE ABILITIES COURSE OUTCOMES CO1 REMEMBERING Recall fundamental definitions, notations, and basic properties related to real numbers, sequences, series, and functions. CO2 UNDERSTANDING Explain key concepts such as convergence, limits, continuity, and differentiability using appropriate examples and counterexamples. CO3 APPLYING Apply standard theorems and techniques of real analysis to solve problems involving sequences, series, limits, and continuous functions. CO4 ANALYSING Analyze mathematical statements to determine convergence, continuity, and differentiability by examining underlying conditions and logical structure. CO5 EVALUATING Evaluate transformations, roots, and functional behaviors in the complex plane to test conformality and angle preservation. CO6 CREATING Evaluate the validity of mathematical arguments and proofs in real analysis and justify conclusions using rigorous reasoning.
