This course covers Riemann and Lebesgue integration in n dimensions, differential forms, determinants, and Stokes's theorem. Students are required to learn twenty important proofs. It is designed for students with a strong interest in pure mathematics or physics. Students whose primary interest is in computer science, statistics, or data science will probably find MATH E-23c a more appropriate alternative. Students may not receive degree credit for both MATH E-23b and MATH E-23c.