1. 授業目的・方法

目的：大学院初学年でのミクロ，マクロ経済理論の理解に必要な数学と応用例を講義します。

方法：担当教員による講義及び毎週の宿題

2. 授業内容

第1-2週 ユークリド空間と１次独立性  [SB, chs. 10-11]

第3-4週 実数の連続性とコンパクト集合 [SB, ch. 12]

第5-6週 多変数関数と微分 [SB, chs. 13-14]

第7-8週 陰関数と導関数 [SB, ch. 15]

第9-10週２次形式と行列，凹関数と準凹関数 [SB, ch. 16]

第11週 非線形最適化 [SB, ch. 17]

第12-15週 動学的最適化 [M]

3. 使用教材

Carl P. Simon and Lawrence Blume; Mathematics for Economists, (W. W. Norton, 1994).

[M] Tapan Mitra; “Introduction to Dynamic Optimization Theory” in Optimization and Chaos edited by M. Majumdar, T. Mitra, and K. Nishimura, Springer-Verlag, 2000.

指定図書について:当該学期間，上の教科書を指定図書として，附属図書館カウンターで常時利用できるようにします。

4. 成績評価の方法

期末試験(40%)と宿題(60%)によって評価を行います。

5. 成績評価の基準

　成績は，上記4の方法に基づき，秀（90 - 100点），優（80 - 89点），良（70 - 79点），可（60 - 69点）又は不可（60点未満）により評価し，可以上を合格とします。

6. 履修上の注意事項

予め，Simon and Blume のAppendix A1, Chs. 1-5を理解しておくこと。

1. Course objectives and methods

Objectives: This course is designed to cover the mathematics necessary for micro- and macroeconomic theory at the first year graduate level. Economic applications will also be discussed.

Methods: Lecturing by the instructor together with weekly homework assignments.

2. Course contents

Week #1 - #2: Euclidian Spaces and Linear Independence [SB, chs. 10-11]

Week #3 - #4: Continuity of Real Numbers and Compact Sets [SB, ch. 12]

Week #5 - #6: Functions of Several Variables and Their Derivatives [SB, chs. 13-14]

Week #7 - #8: Implicit Functions and their Derivatives [SB, ch. 15]

Week #9 - #10: Quadratic Forms, Matrices, Concave, and Quasi-concave Functions [SB, ch. 16]

Week #11: Unconstrained Optimization [SB, ch. 17]

Week #12 - #15: Dynamic optimization [M]

3. Teaching materials

Carl P. Simon and Lawrence Blume; Mathematics for Economists, (W. W. Norton, 1994).

[M] Tapan Mitra; “Introduction to Dynamic Optimization Theory” in Optimization and Chaos edited by M. Majumdar, T. Mitra, and K. Nishimura, Springer-Verlag, 2000.

The above two will be reserved at the university library for your reference.

4. Grading policy

A final exam (40%) and homework assignments (60%) determine a course grade for each student.

5. Grading criteria

Each student will be given a passing grade of A (90 -100 pts), B (80 - 89 pts), C (70 - 79 pts), D (60 - 69 pts), or a failing grade of F (0 - 59 pts) according to the above policy 4.

6. Remarks

Enrolled students are expected to have working knowledge of the appendix A1 and chs. 1-5 of Simon and Blume's textbook.