2301520 Fundamentals of AMCS
- Definition of algorithm, Expressing algorithm, Problem specifications, Correctness, Loop invariants, Counter example
- Algorithm performance, Worst-case, Best-case and Average-case analysis, RAM model, Asymptotic notation
- Asymptotic notations and their relationships, Basic algorithm analysis, Recursive algorithm
- Relationship between algorithm and data structure, Abstract Data Type, Dictionaries
- Sorting algorithms, Simple quadratic sorts, O(n log n) sort, Comparison-based sorting algorithm
Syllabus
- 2301520 Fundamentals of AMCS
- Course Description
- Behavioral Objectives
- Learning Contents
- Course Assessment
- Required Text
- Course Plan
- References
Course Description
Mathematical reasoning; computer programming and algorithms; mathematical software systems.
Behavioral Objectives
- Describe and write a mathematical proof related to upper/lower bound of real number, limit of a real-value function and sequences of real numbers
- Analyze algorithms on various data structures
- Design data structure and algorithm to solve a given problem
- Prove algorithm correctness
- Perform asymptotic analysis of a given algorithm
- Analyze the Worst-case analysis, Best-case analysis and Average-case analysis
- Utilize mathematical software to solve problems in applied mathematics and computational science
Mathematical software system
| No. | Date/Time | Contents |
|---|---|---|
| 1 | 1 กรกฎาคม 2557 9:00 – 12:00 น. | Introduction to Mathematical Software |
| 2 | 2 กรกฎาคม 2557 9:00 – 12:00 น. | Power Series and Numerical Approximation |
| 3 | 3 กรกฎาคม 2557 9:00 – 12:00 น. | Data Manipulation and Statistics |
| 4 | 4 กรกฎาคม 2557 9:00 – 12:00 น. | Differential Equation |
| 5 | 7 กรกฎาคม 2557 9:00 – 12:00 น. | Computer Simulation |
| 6 | 8 กรกฎาคม 2557 9:00 – 12:00 น. | Orientation: No class |
| 7 | 9 กรกฎาคม 2557 9:00 – 12:00 น. | Review |
| 8 | 10 กรกฎาคม 2557 9:00 – 12:00 น. | Part I exam |
Computer Programming and Algorithms
| No. | Date/Time | Contents |
|---|---|---|
| 1 | 15 กรกฎาคม 2557 8:30 – 11:30 น. 13:00 – 14:00 น. |
Definition of algorithm, Expressing algorithm, Problem specifications, Correctness, Loop invariants, Counter example Lab 1: Introduction to Python on the web, http://www.sagemath.org |
| 2 | 16 กรกฎาคม 2557 8:30 – 11:30 น. 13:00 – 14:00 น. |
Algorithm performance, Worst-case, Best-case and Average-case analysis, RAM model, Asymptotic notation Lab 2: Python data structure and programming |
| 3 | 17 กรกฎาคม 2557 8:30 – 11:30 น. 13:00 – 14:00 น. |
Asymptotic notations and their relationships, Basic algorithm analysis, Recursive algorithm Lab 3: Function and Class in Python |
| 4 | 18 กรกฎาคม 2557 8:30 – 11:30 น. 13:00 – 14:00 น. |
Relationship between algorithm and data structure, Abstract Data Type, Dictionaries Lab 4: Advanced data structure in Python |
| 5 | 21 กรกฎาคม 2557 8:30 – 11:30 น. 13:00 – 14:00 น. |
Sorting algorithms, Simple quadratic sorts, O(n \log n) sort, Comparison-based sorting algorithm Lab 5: Sorting algorithm in Python |
| 6 | 22 กรกฎาคม 2557 8:30 – 11:30 น. 13:00 – 14:00 น. |
Part II exam |
Mathematical Reasoning
| No. | Date/Time | Contents |
|---|---|---|
| 1 | 23 กรกฎาคม 2557 8:30 – 11:30 น. 13:00 - 14:00 น. |
Logic and methods of proof |
| 2 | 24 กรกฎาคม 2557 8:30 – 11:30 น. 13:00 - 14:00 น. |
Boundednes, Supremum, Infimum |
| 3 | 25 กรกฎาคม 2557 8:30 – 11:30 น. 13:00 - 14:00 น. |
Sequences of real numbers |
| 4 | 28 กรกฎาคม 2557 8:30 – 11:30 น. 13:00 - 14:00 น. |
Limits and Continuity |
| 5 | 29 กรกฎาคม 2557 8:30 – 11:30 น. 13:00 - 14:00 น. |
Review |
| 6 | 30 กรกฎาคม 2557 8:30 – 11:30 น. 13:00 - 14:00 น. |
Part III exam |
Links
Computer Programming and Algorithm lectures
- Definition of algorithm, Expressing algorithm, Problem specifications, Correctness, Loop invariants, Counter example
- Algorithm performance, Worst-case, Best-case and Average-case analysis, RAM model, Asymptotic notation
- Asymptotic notations and their relationships, Basic algorithm analysis, Recursive algorithm
- Relationship between algorithm and data structure, Abstract Data Type, Dictionaries
- Sorting algorithms, Simple quadratic sorts, O(n log n) sort, Comparison-based sorting algorithm