Doctor of Philosophy in Mathematics | Units, Syllabus & Study Materials - YNetStudyHub

Doctor of Philosophy in Mathematics Verified Syllabus

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10 Semester Units 84 Curriculum Topics 3-4 Years Commission for University Education (CUE) Aligned 24/7 AI Tutor Enabled
10 Units
84 Syllabus Topics
3-4 Years Duration
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0 Active Students

Course Units & Curriculum 10 Units

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Abstract Algebra
9 Topics
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1 Applications of Abstract Algebra
2 Group Actions
3 Group Homomorphisms and Isomorphisms
4 Introduction to Groups Free Preview
5 Linear Transformations and Matrices
6 Polynomial Rings
7 Rings and Fields
8 Subgroups and Lagrange's Theorem
9 Vector Spaces
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Past examination papers for this unit are being compiled.
1 Applications of Derivatives
2 Differential Equations
3 Differentiation Techniques
4 Integration Methods
5 Limits and Continuity Free Preview
6 Multivariable Calculus
7 Taylor Series and Maclaurin Series
8 Vector Calculus
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Past examination papers for this unit are being compiled.
1 Curvature and Torsion
2 Curves in Space
3 Differential Forms and Exterior Calculus
4 Geodesics and Minimal Surfaces
5 Introduction to Differential Geometry Free Preview
6 Lie Groups and Lie Algebras
7 Riemannian Geometry
8 Surfaces in Euclidean Space
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Past examination papers for this unit are being compiled.
1 Applications of Functional Analysis
2 Banach Spaces and Hilbert Spaces
3 Distributions and Sobolev Spaces
4 Fourier Analysis
5 Introduction to Functional Analysis Free Preview
6 Linear Operators and Functionals
7 Metric Spaces and Normed Spaces
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Past examination papers for this unit are being compiled.
1 Determinants and Inverses
2 Eigenvalues and Eigenvectors
3 Inner Product Spaces
4 Introduction to Vectors Free Preview
5 Linear Transformations
6 Matrix Operations
7 Orthogonality
8 Systems of Linear Equations
9 Vector Spaces
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Past examination papers for this unit are being compiled.
1 Applications of Mathematical Logic
2 Formal Proofs
3 Gödel's Incompleteness Theorems
4 Inference Rules and Proofs
5 Introduction to Mathematical Logic Free Preview
6 Logical Equivalences
7 Predicate Logic
8 Propositional Logic
9 Set Theory and Logic
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Past examination papers for this unit are being compiled.
1 Diophantine Equations
2 Divisibility Rules
3 Fermat's Little Theorem and Euler's Totient Function
4 Greatest Common Divisor (GCD) and Least Common Multiple (LCM)
5 Modular Arithmetic
6 Number Systems
7 Prime Numbers Free Preview
8 Pythagorean Triples
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Past examination papers for this unit are being compiled.
1 Applications of Probability Theory
2 Bayes' Theorem
3 Central Limit Theorem
4 Combinatorics and Probability
5 Conditional Probability
6 Expected Value and Variance
7 Hypothesis Testing
8 Introduction to Probability Theory Free Preview
9 Probability Distributions
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Past examination papers for this unit are being compiled.
1 Continuity and Differentiability
2 Differentiation in Several Variables
3 Integration in Several Variables
4 Introduction to Real Analysis Free Preview
5 Metric Spaces
6 Sequences and Series
7 Sequences of Functions
8 The Riemann Integral
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Past examination papers for this unit are being compiled.
1 Applications of Topology
2 Continuity and Homeomorphisms
3 Introduction to Topology Free Preview
4 Metric Spaces and Topology
5 Topological Constructions
6 Topological Invariants
7 Topological Properties
8 Topological theorems and Proofs
9 Topology in Different Dimensions
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Past examination papers for this unit are being compiled.

Curriculum Architecture

This program is structured into comprehensive academic units combining theoretical foundations, analytical research, practical tutorials, and continuous assessments. Each unit is mapped to key learning outcomes aligned with higher education qualification frameworks.

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