Unit 5 — Advanced Statistics & Operations Research
Unit 5 of the TRB (Tamil Nadu Teachers Recruitment Board) Mathematics syllabus: Advanced Statistics & Operations Research. Major areas covered: EDA; Linear Models; Multivariate Analysis; Sampling; Design of Experiments; Reliability; Linear Programming; Queueing. Suggested weightage: 20%. Topics include: Gauss-Markov, ANOVA/ANCOVA, Wishart, PCA, LDA, SRS/Stratified, CRD/RBD/LSD, BIBD, 2^k factorials, Simplex, M/M/1, M/G/1.
Chapters
- Exploratory Data Analysis
- Linear Models
- Multivariate Analysis
- Sampling Theory
- Design of Experiments
- Reliability
- Operations Research
TutorDA LMS
Unit 4 — Probability & Statistical Inference
Unit 4 of the TRB (Tamil Nadu Teachers Recruitment Board) Mathematics syllabus: Probability & Statistical Inference. Major areas covered: Descriptive Statistics; Probability; Random Variables; Stochastic Processes; Distributions; Estimation; Hypothesis Testing; Nonparametric Tests. Suggested weightage: 20%. Topics include: Bayes theorem, CLT, LLN, Markov chains, MLE/MOM, UMP tests, LRT, Chi-square, Rank correlation, Bayesian inference.
Chapters
- Descriptive Statistics
- Probability
- Random Variables
- Convergence
- Stochastic Processes
- Distributions
- Estimation
- Hypothesis Testing
- Nonparametric Tests
- Bayesian Inference
TutorDA LMS
Unit 3 — Differential Equations & Mathematical Methods
Unit 3 of the TRB (Tamil Nadu Teachers Recruitment Board) Mathematics syllabus: Differential Equations & Mathematical Methods. Major areas covered: ODE; PDE; Numerical Analysis; Calculus of Variations; Integral Equations; Classical Mechanics. Suggested weightage: 20%. Topics include: Existence-uniqueness, Sturm-Liouville, Green's function, Lagrange-Charpit, Separation of variables, Newton-Raphson, RK methods, Euler-Lagrange, Fredholm/Volterra, Hamiltonian dynamics.
Chapters
- Ordinary Differential Equations
- Partial Differential Equations
- Numerical Analysis
- Calculus of Variations
- Linear Integral Equations
- Classical Mechanics
TutorDA LMS
Unit 2 — Complex Analysis, Algebra, Topology, Functional Analysis
Unit 2 of the TRB (Tamil Nadu Teachers Recruitment Board) Mathematics syllabus: Complex Analysis, Algebra, Topology, Functional Analysis. Major areas covered: Complex Analysis; Combinatorics; Number Theory; Group/Ring/Field Theory; Galois Theory; Topology; Banach & Hilbert Spaces. Suggested weightage: 20%. Topics include: Analytic functions, Contour integration, Residues, Mobius maps, Sylow theorems, Ideals, UFD/PID/ED, Galois groups, Compactness, Spectral theorem.
Chapters
- Complex Analysis
- Algebra (Combinatorics & NT)
- Group Theory
- Ring Theory
- Field Theory
- Topology
- Functional Analysis
TutorDA LMS
Unit 1 — Analysis & Linear Algebra
Unit 1 of the TRB (Tamil Nadu Teachers Recruitment Board) Mathematics syllabus: Analysis & Linear Algebra. Major areas covered: Real Analysis; Linear Algebra. Suggested weightage: 20%. Topics include: Set theory, Real numbers, Sequences/Series, Continuity, Differentiability, Riemann & Lebesgue Integration, Multivariable Calculus, Metric Spaces, Vector Spaces, Matrices, Eigen-theory, Canonical Forms, Inner Product, Quadratic Forms.
Chapters
- Real Analysis
- Linear Algebra
TutorDA LMS