Math 151. Analysis I
(not advised for non pure math students)

Axiomatic treatment of real numbers and its properties. Uniqueness of the real number system. Natural numbers, integers, rational numbers. Polynomial and rational functions over ℝ. Vector spaces over ℝ. Euclidean space ℝⁿ, angle, sin and cosine. Complex numbers. Abstract metric spaces. Rudiments of topology. Sequences in an arbitrary metric space. Limits (with formal proofs). Bolzano-Weierstrass Theorem. Completeness of ℝ. Nested Interval Property. Divergence to ∞. Limit inferior and superior. Series in an Euclidean space. Alternating series. Absolute convergence. Criteria of convergence. Power series. Radius of convergence. Sequences of functions, pointwise convergence. Limit and continuity (formal). Mean Value Theorem. Differentiation. Rules of Differentiation. Rolle’s Theorem. L’Hospital’s Rule. Curve sketching, maxima and minima. Banach spaces and algebras.

Prerequisite: Consent of instructor for non-Math students.

Core for Math.