Jump to Part II: Analysis.## Syllabus MA347/MA348 Spring 2016

## This final revision W15 2016

\begin{document} \maketitle## Introduction

This file is frequently updated. Check the date for the last two edits and reload your browser pages each time you visit. Note the convention that F1 means "Friday of Week 1" (we use R for Thursday, and S for Saturday). Label every course submission by this day-week code for when due, even if it is late or has been postponed. Most lessons have a filecard linked to the text. Just filling out these embedded questions when they are due will earn you half-credit for your lesson-preparation. Additional credit for correct answers. But late and correct answers still receive half-credit. This counts towards yourclass participationIP score, which is a substantial portion of your grade.## Announcement

Since the syllabus is most reliable and up to date guide to the course, new folders and other useful information are linked here for quick reference . These include

- Essays on writing mathematics
- Optional lessons on Python arithmetic
- Additional Advice
## Part I Discrete Mathematics

\section{Lesson 1 Numbers, Sets and Functions} \begin{itemize} \item [W1] Numbers Commentary on D'Angelo-West Chapter 1 begun. AGHM inequality, arithmetic and geometric proofs. \\ \item [F1] Commentary on D'Angelo-West Chapter 1 completed. Introduction to online Advice and how to find it when you need it. \\ \item [M2] Submit Homework 1 on assessing problem sets. \item [M2] Lesson on writing math on homework and tests. \item For the benefit of students without access to the text, or to a different edition, here is a PDF scan of the problems in question. Please use only the numbering given here when referencing the problems.\\ \end{itemize} \section{Lesson 2 Language and Proofs } \begin{itemize} \item [W2] Concerning Grades reprinted from Piazza \\ \item [W2] Summary of lesson on logic. \\ \item [W2] Logical Language Commentary on D'Angelo-West Chapter 2 \\ \item [W2]More Advice on Common Logic as it pertains to mathematics.\\ \item [F2] Material Implication with the texPad typesetting tool for mathematical expressions. \\ \item [M3] Quiz 1 on Lesson 1 of the course. You may use your Journal as sole resource. \item [W3] Logic Homework 2 is due. \\ \end{itemize}

## Schedule of Tests and 348Project deadlines.

\begin{itemize} \item [M3] Quiz 1 \item [M4] 348Project Draft Proposal due \item [M5] Quiz 2 \item [M6] 348Project Proposal due \item [M7] Midterm \item [M8] 348Project Progress Report due \item [M9] Quiz 3 \item [F9] 348Project First Draft due \item [M10] Quiz 4 \item [M13] 348Project Final Draft due \item [M13] Quiz 5 \item [F15] Conflict Final \item [T16] Final \end{itemize} \section{Lesson 3 Induction} \begin{itemize} \item [W3] Induction Commentary on D'Angelo-West Chapter 3 \\ \item [F3] Peer seminar on the Mathematical Induction problem set.\\ \item [M4] Induction Homework 3 is due.\\ \item [M4] Return and discussion of Quiz 1.\\ \item [T4] Infosheets are now past due! Download infosheet.png , print, and fill out.\\ \end{itemize} \section{Lesson 4 Bijections and Cardinality} \begin{itemize} \item [W4] Cardinality Commentary on D'Angelo-West Chapter 4 \item [F4] Koenig's proof of the Cantor-Bernstein-Schroeder Theorem \item [F4] Introduction to Cantor's Cardinality Theorems . \end{itemize} \section{Lesson 5 Cantor's Cardinality Theorems} \begin{itemize} \item [M5] Quiz 2 on Lessons 2 and 3. You may use your journal as your sole reference. \item [M5] Review of CBS-Theorem, John Horton Conway's proof. \item [W5] Conclusion of Cantor's Cardinality Theorems with filecard. \item [W5] Introduction to divisibility, long division, Python. \item [F5] Return and Discussion of Quiz 2 and old homework. Preview. \end{itemize}

## Note, D'Angelo-West Ch. 5 is not treated in this course.

\section{Lesson 6 Euclid's Algorithm [D'Angelo-West Ch.6]} \begin{itemize} \item [M6] Euclid's algorithm and Diophantine equations with embedded filecard questions. \item [W6] Method for solving Diophantine Equations using Jim Carlson's algorithm. \item [F6] Review for Midterm. \item [M7] Midterm \end{itemize} \section{ Lesson 7 Modular Arithmetic [D'Angelo-West Ch.7]} \begin{itemize} \item [W7] Lesson on Modular Arithmetic and Fermat's Little Theorem begun. \item [F7] Homework 5 is due. Please bring a printed copy of the homework with you to class. We will go over (most) of the problems in class, but "exchange papers" for peer editing. If this works with the classit will not only speed up the turn-around of the homework, but also lead to better class discussion. \item [M8] Lesson on Modular Arithmetic and Fermat's Little Theorem concluded. \end{itemize} \section{ Public Key Encryption } \begin{itemize} \item [W8] RSA Public Key Encryption . \item [M9] Quiz 3 on Lessons 6 and 7. \end{itemize}

## Part II Continuous Mathematics

\section{Definitions of the Real Numbers} \begin{itemize} \item [W9] Lesson A1: Definition of a Real Number with filecard. \item [F9] Lesson A2: Seminar on Bounded Sets. \item [M10] Return and discuss Quiz M9. Regraded requests due F10. \item [W10] Quiz and Seminar on Bounded Sets \item [F10] Seminar on Bounded Sets concluded \item [M11] Homework on Bounded Sets is dues at class time. No late homework accepted. \item [M11] Filecards for W9 Lesson A1 and W11 Lesson A3 due M11. Will be graded. \item [M11] MA348 mandatory class on the Semester Project. Excuse for absence must be obtained before class. \item [M11] MA347 No class today. \item [W11] Lesson A3: Limits of Sequences and Series with filecard. \item [F11] Seminar on Limits . \item [M12] Lesson A5: The Bolzano-Weierstrass Theorem with filecard. \item [F12] Summary and Review on analysis lessons. \item [M13] Quiz on analysis. \item [M13] MA348 Class Project is Due. \item [W13] Lesson A6: Null Functions, Limits, Continuity, Derivatives, Chain Rule with filecard. \item [F13] Applications to the various Intermediate Value Theorems. \item [M14] Return and discussionof Quiz M13. Regrades due F13. \item [W14] Bolzano's Intermediate Value Theorem \item [F14] Review for the final of the analysis half of the course. \item [F14] Notes on the Toeplitz Sequence Defining e \item [F14] If you have been invited to submit your Journal for consideration to replace missed tests and work in the course, this must be submitted today so that it can be returned on M15. \item [M15] Review for the final of the algebra half of the course. Mandatory attendance.. \item [T15] Walk-in Office Hours at Atlas House 1:30-3:30. All work for the sememester must be submitted by T15 to receive any consideration for credit other than the final. \item [W15] Last class. Mandatory attendance. \item [W15] Essay topics to prepare for the final will be handed out in class. These will not be posted online. \item [F15] Three hour, handwritten conflict final 8am in 343 AH. Make personal arrangements with instructor by email to take this exam before M15. \item [T16] Three hour, handwritten final for both MA348 and MA347 8am in room 239AH . \end{itemize} \end{document}