MAD 2502 Introduction to Computational Mathematics

MAD 2502 Introduction to Computational Mathematics (Spring 2018)

Instructor: Dr. Shi Bai
Office: Science Building (SE43), Room 230.
Email: sbai@fau.edu
Lecture time and location: W F 9:30-10:50AM in SE 271.
Office hours: Wed 2 - 3 pm; and by appointment; and lab session (Wed 4 - 5 pm; Fri 2 - 3 pm).
Syllabus and Textbook: John V. Guttag, Introduction to Computation and Programming Using Python. 2nd Ed. (The FAU library has e-book access available for FAU students.)
~~Mid-exam: 9:30am-11:00am, Mar 2 (Fri). Room: SE 271.~~
Final exam: Wed (May 2) 7:45am - 10:15am. Room: SE 271.

General information

Suggestion: please read, review and understand the codes discussed on the lecture. Here are some more detailed suggestions:

After the first several weeks, you should know the basics of Python including: integer, float, string types; print and input functions; conditional argument; for and while loop; lists; functions.
The fundamental barrier is to understand what happens as the computer executes each line of the code (in particular, those in the loops or branches). To pass this course, it is important to understand the algorithms discussed on the class Line-by-Line, ensuring you understand what each line is precisely doing. A vague/imprecise understanding is not enough.
In the beginning, it's not a surprise to expect to spend 6-10 hours to fully understand a tiny piece of program/code consisting of (e.g.) 10 lines. Such efforts/time should be expected.

Here are some more websites for tutorials/exercises.
  Interactive tutorial (snakify.org)
  Python Tutorial
  Project Euler (more mathematical/computational problems)
Tutorials/Lab sessions: Wed 4-5pm and Fri 2-3pm in SE 271. Please consider to come to the tutorial session if you need hands-on guide.
Quizzes: there will be ≥ 5 quizzes. But only your best 5 quizzes will be taken into account towards your final grade; the others will be dropped.
Open Computer Labs: the following open computer labs have Python installed: UN 222 (Student Union), BU 201 (College of Business) and CM 142 (Computer Center).

Schedule

The course covers topics and examples in numerical algorithms, number theoretic algorithms, combinatorics, algebra, cryptography and misc topics.

	Chapters	Topics	Algorithms and extra	Codes	Annoucements
Week 1	Chap 2.1-2.4	Python basics: numeric data types, strings, variables, IDLE.	IDLE	Lecture 1 Operators Lecture 2 Input
Week 2	Chap 3.1-3.3; Chap 9	Intro to algorithms, algorithmic complexity.	Computing/approx square/cubic root.	Lecture 3 Lecture 4	Quiz 1
Week 3	Chap 4.1-4.2	Functions in Python.	Bisection method (read this and this).	Lecture 5 Scope Bisection	Quiz 2
Week 4	Chap 3.4 Chap 5.1-5.5	Algorithmic complexity; Python structured types: tuples and lists.	Horner's method (read this).	Horner's method Bisection with Horner	Assignment 1 (Due Feb 5th, 5pm)
Week 5	Chap 3.5.	Root-finding algorithms.	Newton's method (read this and animations).	Newton's method	Quiz 3
Week 6	Chap 4.3	More numerical algorithms; Recursion.	Numerical diff. (read this); Secant method (read this and animations); Factorial, Fibonacci sequence (read this); binomial coefficients (read this).	Secant method Recursion	Quiz 4
Week 7		Floating-point numbers	Floating point numbers (read this and this);	Floating-point numbers	Assignment 2 (Due Feb 26th, 5pm)
Week 8	Chap 15/16	Random number generator; simulating games.	Coin flipping; Birthday paradox (read this); Monty hall problem (read this).	Coin flipping Birthday paradox Monty hall	Mid-exam (Friday 9:30-11:00am)
Week 9 (spring break)
Week 10		Solution to mid-exam			Assignment 3 (Due Mar 21, 5pm)
Week 11		Topics in number theory	Detecting primes (read this); Sieve of Eratosthenes (read this); Euclidean algorithm (read the procedure).	Primality tests; Euclidean alg.	Quiz 5
Week 12		Topics in number theory and cryptography	Modular arithmetic (read this); Trial division (read this); Pollard's rho method (read this);	Trial division; Pollard's rho method.	Quiz 6
Week 13	Chap 10	Search and sort .	Binary search (try this); Selection and merge sort (read this and this).	Binary search; Sorting.	Assignment 4 (Due Apr 5th, 5pm)
Week 14	Chap 12	Topics in cryptography	0-1 Knapsack Problem (read this); Meet-in-the-middle attack (read this).	0-1 Knapsack.	Quiz 7 (Wed)
Week 15			Review sessions		Quiz 8 (Wed)
Exam week (April 26 – May 2)

Documentation:
  Python 3 documentation -- Official Website
  A Gentle Introduction to Programming Using Python MIT Open Courseware.
  Visualize Python Execution
  Mathematical Computation with SageMath
  Differences between Python 2.7.x and Python 3.x
  Python on Windows FAQ

IDLE:
One Day of IDLE Toying
Intro to Python IDLE