Course Overview • The real number system • Metric spaces and basic topology • Sequences and series • Continuity • Topics from differential and integral calculus Grading Homework assignments 20% Quiz (Feb. 9) 5% Midterm 1 (Mar. 9) 20% Midterm 2 (Apr. 13) 20% Final (May. 10 7:45-9:45 AM) 35% A ≥90% B ≥80% C ≥70% D ≥60% Tutoring • Tom Stone @VV B205 • Monday 2:30 - 4:30 PM • Tuesday 2:00 - 4:00 PM What is Analysis • Proof • How calculus works • Fundamental axioms Number Systems • Natural Numbers: N={1,2,3,…} • Integers: Z={0,±1,±2,±3,…} • Rational Numbers: Q={a/b│a,b∈Zb≠0} • Real numbers R: fill the “holes” in the rational numbers √2 is not rational • There is no rational number p such that p^2=2 • Proof by contradiction • Assume there is a rational number p such that p^2=2 • Then p=m/n , where m,n∈Z, n≠0, and m,n have no common factor • (m/n)2=2⇒m2/n^2 =2⇒m2=2n2 • So m is even • m=2k (k∈Z⇒(2k)2=2n2⇒4k2=2n2⇒2k2=n2 • So n is also even • m,n are both division by 2 • This contradicts the fact that m,n have no common factor • So no such p exists
