26sep08  Syllabus
Math 348 F08  "Advanced Composition in Fundamental Mathematics"
Texts: Liebeck, A Concise Introduction to Pure Mathematics", 2nd ed.
       Toeplitz, The Calculus: A Genetic Approach, any edition
Instructor: George Francis, section C1, 10MTWF, 143 AH.
Bookmark: http://new.math.uiuc.edu/math348/  
for calendar, updates, notes and frequently asked questions (FAQ). 
Key: DayWeek labels, thus W2 is Wednesday of Week 2. 
Text is labeled [Xy] for X=L/T, and y is the chapter/section.  
Assigned exercises are labeled thus <x.y>. and are due 2 class periods 
        after assignments. For now, and until we have a grader, enter 
        a clean copy of your solutions into your journals.
Part I (6 weeks) Discrete Mathematics (L1, L8, L11-16)
M1 Introductory Lecture and Course Outline.
   Lesson: [L1] Symbolic logic and mathematical notation. 
   < L1.5,6,7> due W1.
T1 Lesson: [L1 and webnotes]Propositional Logic and Truth Tables 
   <webnotes.1,2,3,4> due F1. 
W1 Material implication, quantifiers and proofs by contradiction. [L1] 
F1 Review of Week 1 and discussion of assigned problems.
M2 Labor Day. No classes.
Homework TBA later. Check this page.
T2 Mathematical induction [L8]  
W2 Strong induction, prime factorization [L8]
F2 Introduction to LaTeX [room 239 AH]
M3 Quiz 1 (20min) 
   Lesson: Euclid's Algorithm [L11]
T3 Euclid's Algorithm, GCD (aka hfc), 
W3 Prime Factorization Theorem (aka Fundamental Theorem of Arithmetic) [L12]
F3 Introduction of Python programming [239 AH]
M4 Quiz 2 (20min) 
   Lesson: Sieve of Eratosthenes 
T4 Congruence relations [L14]
W4 Clock arithmetic and finite fields [L14]
F4 Computer Lab
M5 Solving linear congruence equations. 
T5 Seminar: reports and solving problems at the blackboard
W5 Fermat's Little Theorem
F5 Review of material through M5.
M6 Applications of FLT [L15]
T6 Hourly Test 1  (50 min)
W6 RSA public key codes [L16]
F6 Computer Lab
Part II Continuous Mathematics [Toeplitz T6-10, T23-27, T36, T40-42]
M7 Decimals and geometric series [T6 and L3]
T7 Continuous compound interest and the numer e [T7]
W7 continued
F7 Computer Lab
M8 Quiz 3 (20 min)
   Lesson: periodic decimasl [T8 and L4]
T8 The field of rational numbers [L2]
W8 The irrational numbers [L2]
F8 Computer Lab 
M9 Convergence and limits of sequences and series [T9 and T10]
T9 Seminar on real numbers
W9 Seminar on limits 
F9 Computer Lab 
M10 Quiz 4 (20 min) 
    Lesson: Fundamental Theorem of the Calculus  [T23]
T10 Proving the rules of differentiation from its definition 
W10 The product rule and integration by parts [T24, 25]
F10 Computer Lab
M11 The chain rule and Leibniz' differential calculus [T26]
T11 Integration by subsitution [T27]
W11 Quiz 5 (20 min)
    Lesson: Newton's mechanics, velocity and acceleration [T36]
F11 Computer Lab
M12 Newton's Law of Gravitation derived from Kepler's laws.
M12 Derivation of Kepler's laws from Newton's Law of Graviation
M12 Kepler's 3rd Law.
F12 Computer Lab
M13 Concluding remarks on mechanics 
T13 Seminar on mechanics
W13 Review for test
F13 Hourly Test 2 (50 min) 
Thanksgiving Vacation
M14-W15 TBA 
Final examination 8am Friday 19 December 2008. This course has no 
conflict final. Do not plan to leave town before the exam.