Course Objectives
At the completion of this course, students will be able to
1) perform calculations of permutation and combination,
2) solve problems of arithmetic sequence and geometric sequence,
3) calculate sums of sequence using sigma symbol,
4) understand recurrence relation and mathematical induction.
Rubric
| Ideal Level | Standard Level | Unacceptable Level |
| Achievement 1 | Can perform complicated calculations of permutation and combination. | Can perform basic calculations of permutation and combination. | Can't perform basic calculations of permutation and combination. |
| Achievement 2 | Can solve complicated problems of arithmetic sequence and geometric sequence. | Can solve basic problems of arithmetic sequence and geometric sequence. | Can't solve basic problems of arithmetic sequence and geometric sequence. |
| Achievement 3 | Can calculate complicated sums of sequence using sigma symbol. | Can calculate basic sums of sequence using sigma symbol. | Can't calculate basic sums of sequence using sigma symbol. |
| Achievement 4 | Can understand and use recurrence relation and mathematical induction. | Can understand recurrence relation and mathematical induction. | Can't understand recurrence relation and mathematical induction. |
Assigned Department Objectives
Teaching Method
Outline:
As a basis for natural science and engineering, students will learn about calculations of permutation and combination, arithmetic sequence and geometric sequence, sums of sequence using sigma symbol, recurrence relation and mathematical induction, etc.
Style:
Lectures, exercises, and assignments.
Content of the lectures gradually increases in quantity and quality, compared to junior high school. We recommend that students prepare for each lectures.
If there is anything you do not understand in the lectures, please review it immediately and try to understand it. Active questions are always recommended.
It is not enough to understand basic contents once. Please train repeatedly.
The lectures plan may be changed according to the student's level of understanding.
Notice:
Evaluations will be made comprehensively by written exams (making up about 90% of the grade), by exercises and homework (making up about 10% of the grade).
Can take makeup exam in need aid up to maximum of 50 points.
Characteristics of Class / Division in Learning
Course Plan
|
|
|
Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Number of cases |
Dendrogram, law of sum, law of product
|
| 2nd |
Permutation |
Permutation, factorial, permutation formula
|
| 3rd |
Permutation, combination |
Repeated permutation, combination
|
| 4th |
Combination, various permutations |
Combination, permutations of multi sets
|
| 5th |
Various permutations, binomial theorem |
Circular permutation, binomial theorem, binomial coefficient, Pascal's triangle
|
| 6th |
Probability, expected value |
Probability, expected value
|
| 7th |
Exercises |
|
| 8th |
Intermediate examination |
|
| 2nd Quarter |
| 9th |
Review and commentary on the intermediate examination |
First term, last term, general term.
|
| 10th |
Arithmetic sequence |
Common difference and sum of arithmetic sequence
|
| 11th |
Geometric sequence |
Common ratio and sum of geometric sequence
|
| 12th |
Summation of sequence |
Definition and calculation of summation using sigma symbol
|
| 13th |
Recurrence relation |
Derivation of general term from recurrence relation
|
| 14th |
Mathematical induction |
Proof based on mathematical induction
|
| 15th |
Final examination |
|
| 16th |
Review and commentary on the final examination |
|
Evaluation Method and Weight (%)
| Examination | Presentation | Mutual Evaluations between students | Behavior | Portfolio | Other | Total |
| Subtotal | 90 | 0 | 0 | 0 | 0 | 10 | 100 |
| Basic Proficiency | 90 | 0 | 0 | 0 | 0 | 10 | 100 |
| Specialized Proficiency | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Cross Area Proficiency | 0 | 0 | 0 | 0 | 0 | 0 | 0 |