Rigorous foundations of calculus with proofs
Foundations of mathematical logic and set theory
Constructing and understanding the real number system
Convergence, limits, and properties of sequences
Infinite series and convergence tests
Open sets, closed sets, compactness, and connectedness
Derivatives, Mean Value Theorem, and applications
Riemann integration and the Fundamental Theorem
Pointwise and uniform convergence of function sequences
Additional advanced topics in analysis
Review and synthesis of course material