Pure Mathematics CSS Syllabus 2025 (in PDF as well)

Download Pure Mathematics CSS Syllabus 2025 in PDF or view online. Pure Mathematics is really a good scoring CSS optional subject that candidates can go for. But, if you are not a science type guy and find interest in social science CSS subjects, you must look for another option.

Pure Mathematics Syllabus (CSS – FPSC)

Section A (40 Marks)

1. Modern Algebra:
   • Groups and subgroups
   • Lagrange’s theorem
   • Cyclic groups
   • Normal subgroups
   • Quotient groups
   • Fundamental theorem of homomorphism
   • Isomorphism theorems of groups
   • Inner automorphisms
2. Linear Algebra:
   • Vector spaces
   • Subspaces
   • Linear independence and dependence
   • Bases and dimensions
   • Linear transformations and their matrices
   • Change of basis
   • Rank and nullity
   • Eigenvalues and eigenvectors

Section B (60 Marks)

1. Calculus:
   • Limits and continuity
   • Differentiation and integration of functions of one and several variables
   • Partial derivatives
   • Multiple integrals and their applications
   • Sequences and series
   • Uniform convergence
2. Real Analysis:
   • Properties of real numbers
   • Sequences and series of real numbers
   • Continuity, differentiability, and integrability of functions
   • Riemann integral
   • Improper integrals
3. Complex Analysis:
   • Complex numbers
   • Analytic functions
   • Cauchy-Riemann equations
   • Complex integration
   • Cauchy’s theorem and integral formula
   • Taylor and Laurent series
   • Residue theorem and its applications

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