Find all real solutions of the differential equations in Exercises 1 through 22./ " ( 0 - 4 / '( 0 + 13/(0 = 0

Week 1 Lecture 1 (1/12/2016) Introduction: Ring theory essentially generalizes the ideas familiar to us through our knowledge of the integers. We shall see some theorems and proofs. Well-Ordering axiom: This axiom states that every non-empty set of non-negative integers contain a smallest element. This axiom is helpful in many of the proofs that we will be learning next. Division Algorithm: Let a, b ∈ ℤ, b>0, then there exists unique integers q, r with the property that 1. a=bq+r 2. 0≤r