Syllabus
Book we follow (free!): "Primer of Real Analysis" by Dan Sloughter
Student produced flashcards for definitions
Homework
For Exam 1 (final revisions due 14 September at 11:59PM)
HW1 (due Monday 26 August) [soln]: Exercises 1.1.3, 1.1.4, 1.3.3, 1.3.4 (b-d), 1.3.6, 1.3.8, 1.3.11
HW2 (due Monday 2 September): Exercise 1.3.3, 1.3.4 (b-d), 1.3.6, 1.3.8, 1.3.11, 1.4.6(b,c), 1.4.9, 1.4.10, 2.1.1, 2.1.2, 2.1.6, 2.1.7, 2.1.10, 2.1.12, 2.1.14, 2.1.17, 2.1.18, 2.1.19, 2.1.21, 2.1.23, 2.1.24, 2.1.26
HW3 (due Friday 6 September Saturday 7 September): 1.3.10, 1.3.11, 1.4.1, AND write a proof that $\displaystyle\lim_{n \rightarrow \infty} \dfrac{n+3}{n+2} = 1$. (on last one, you can "work backwards" as I showed in the lecture to find the $N$ that you need)
For Exam 2
HW4 (due Wednesday 18 September):
HW5 (due Monday 23 September):
HW6 (due Monday 30 September):
HW7 (due Monday 7 October):
HW8 (due Friday 11 October):
For Exam 3
HW9 (due Wednesday 23 October):
HW10 (due Monday 28 October):
HW11 (due Monday 4 November):
HW12 (due Friday 8 November):
For Final Exam
HW13 (due Wednesday 27 November):
HW14 (due Monday 2 December):
HW15 (due Friday 6 December):
Quizzes
Quiz 1 (due 23 Aug) [soln]: Let $A=\left\{ \text{green}, *\right\}$ and $B=\left\{A,4\right\}$. Compute $A \cup B$, $A \cap B$, $A \times B$, and $B \times A$.
Quiz 2 (due 23 Aug) [soln]: Show that the relation $R$ on $\mathbb{Z}$ defined by $m \sim_R n$ iff $m-n$ is even is a transitive relation.
Quiz 3 (due 27 Aug) [soln]: Show that for all $a,b,c \in \mathbb{Q}$ that $a(b+c)=ab+ac$ (and cite relevant equation numbers).
Quiz 4 (due 29 Aug) [soln]: Turn the proof sketch in the notes (see teams) that it is impossible for both $a>0$ and $a=0$ in $\mathbb{Q}$ into a nice proof.
Quiz 5 (due 2 Sep 3 Sep): Turn the proof sketch in the notes (see teams) that $|a-b| \geq 0$ into a nice proof.
Quiz 6 (due Sat 7 Sep): Consider the sequence $a_n=\dfrac{2n+1}{n+2}$. Prove that $\displaystyle\lim_{n \rightarrow \infty} a_n=2$. In your proof, you can choose $N$ so that $N+2 > \dfrac{3}{\epsilon}$.
Exams
Exam 1
Exam 2
Exam 3
