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 your 
class participation IP 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}
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