Practical Teaching Methods of Linear Algebra for Students in the Economics Course

To analyze the big data on web or so, a new type teaching methods of linear algebra is required. In the paper, three requirements for the new teaching method are discussed. They are realated to (1) Vectornotation based expression transformation, (2) eigenvalues of a variance-covariance matrix, and (3) visualization of multivariant analysis

Visualization of Conjugate Distributions in Latent Dirichlet Allocation Model

In Bayesian probability theory, if the posterior distributions p(θx) are in the same family as the prior probability distribution p(θ), the prior and posterior are then called conjugate distributions, and the prior is called a conjugate prior for the likelihood function. In the Latent Dirichlet Allocation model, the likelihood function is Multinomial and the prior function is Dirichlet. There the Dirichlet distribution is a conjugate prior and then the posterior function becomes also Dirichlet. The posterior function is a parameter mixture distribution where the parameter of the likelihood function is distributed according to the given Dirichlet distribution. The compound probability distribution is, however, complicated to understand and have the image. To make many persons understand the image intuitively, the paper visualizes the parameter mixture distribution

スイロン エンジン オ ベース トシタ ケイエイ スウガク キョウジュ ホウ ト ソノ アンケート ヒョウカ

筆者の経営数学の講義では，学生に推論エンジンをシミュレーションさせる教授法「推論エンジンシミュレーション法（Inference Engine Simulating Method）」を行っている。本方法においては、学生にまず2 種類のルール・データベースを頭の中に構築してもらう。ひとつは数学公式をルールとする，数学ルール・データベースである。もうひとつは，経済・経営に関するルール・データベースであり，経済・経営に関するセオリーがルールとして蓄積されている。経営に関する文章題が与えられた場合，推論エンジンシミュレーション法では，第一に，文中の重要キーワードを探し，そのキーワードを使って，2 種類のルール・データベースを検索し，関連するルールを収集する。そして，そのルールの集合に対して,演繹推論を行い，文章題で与えられたデータと,未知数との間の関係を求めていく。本稿では,筆者の経営数学1 の講義においてこの推論エンジンシミュレーション法を用いた結果，学生の学習効果がどれほど向上したかをアンケートにより調査する。In my business mathematics class, I conduct my original heuristics titled “Inference Engine Simulating Method" so that students can solve mathematics problems by simulating the inference engine system. In the method, the students in advance have to construct two kinds of rule databases in their heads; one is a mathematics rule database where mathematics formulas are stored and another is an economics rule database where economics theories are stored. Given a mathematics word problem, the students will firstly find the most important keyword among the words. Then with the keyword, they will retrieve the rule databases to collect the related rules. Secondly, the students conduct the deductive reasoning on the rules to find the relationship between the given data in the problem words and the unknown. In my business mathematics lectures, I have used this Inference Engine Based Instruction Method. To analyze the effects of this method, I conducted the questionnaires in my class. The results will be shown in the paper

スウガクヨウ Web キョウザイ ジドウ セイセイ ノ タメノ キョウザイ ナイヨウ ノ イミ ニカンスル XML タグ テイギ

本稿では，マクロ経済学において重要な国民所得決定モデルを説明するWeb教材を事例として，我々の開発するe-Math Interaction Agentという数学用Web教材自動生成システムを紹介する。本システムは人間に代わってXMLファイルを生成するが，本論文では，数学用マルチメディア教材定義について必要となるXMLタグが，レイアウト定義用と問題の意味定義用の2種類必要であることを説明し，国民所得決定問題において定義した意味的XMLタグを説明する。こうした問題の意味的タグ定義は仮想教師のガイダンス中，特定の数式及び変数間の関係を言葉，2次元あるいは3次元のグラフなど各種の表現方法で説明する場合に必須である。In the paper, Web-based learning materials for a national income determination problem in macroeconomics are presented as sample materials for explanation of our developed mathematical courseware automation system named e-Math Interaction Agent. This system automatically generates target XML files instead of human programmers. In the paper, it is described that there are two kinds of XML tags should be defined for the automation. One is defined for a Web page layout and another is for definition of semantics in the given mathematical problem. This semantic definition is required for generation of higher qualitative virtual teacher\u27s guidance so that the teacher can explain semantics of an equation or a relationship between two variables in various expressions such as words, 2 or 3 dimensional graphs

Methodologies for the Automation of Web-Based Interactive Courseware for Mathematics

In this paper, we describe the newest version of our mathematical e-learning material generation system, e-Math Interaction Agent 2. Its key feature is the simplicity of its solution plans and presentation definitions. The presentation layers are completely separated from the pure mathematical solution processes, significantly increasing the reusability of the definitions

Instruction Methods for Solving Word Problems in Mathematics Education

The purpose of this paper is to report on three methodologies that I practise in business mathematics lectures. In business mathematics, a problem to find is more important than a problem to prove. Thus, my target is a problem to find. The first methodology is to solve a problem visually to the extent possible, not only using existing algebraic methods but also a visual method that includes mathematical software, such as Maple and Mathematica. In business mathematics today, problem solving using the visual approach is more important than that using the algebraic approach because business requires the speedy modeling of the target and prompt analysis of the model. Thus we can say that the visual solution skill is also required as digital literacy in the business mathematics field. Therefore, lecturers are recommended to take greater advantage of this new visual approach. The second methodology is to practise Polya’s famous heuristics, described in his book, “How to Solve It”. It is particularly important for students to first write down the given data and the unknown to understand a word problem. The third methodology is to have students construct rule databases in their heads to make a deduction. Using deduction, they can easily find the connection between the given data and the unknown to devise a solution plan. Based on my experience with deductive database system construction, I think that the procedures used in a deductive system can be applied to students’ solution procedures. In my lectures, I repeatedly teach students deductive patterns. Thinking patterns using these three methodologies are helpful in cultivating students’ ability to solve future problems by themselves

ブラック ショールズ ホウテイシキ ニカンスル シミュレーション ト グラフィクス ニヨル コウサツ

　学生にとって難解と思われているブラック＝ショールズ方程式であるが，視覚的にグラフィクス表現することで，理解が容易になる。本稿では，その確率的ブラウン運動を含む確立微分方程式に関するシミュレーション実験結果と代数学的に求められる理論的結果を3次元グラフィクスにより示す。確率的現象をコンピュータ上に再現することで，確率的ブラウン運動の理解が容易になり，同時に理論的に求められる正規分布を示し両者を比較することで，理論的事柄の理解を深める。また，オプションの期待値の導出過程における，期待値計算の積分計算範囲を，正規分布に伴う確率変数と対数正規分布に従う確率変数に関して，両者同時にグラフィクスで視覚的に示す。本稿のグラフィクスの特長は，変数間の関係をスライダー操作によるモーションとして表現した点である。スライダーで変数を動かすことにより，複雑な関係式における他の変数への影響の理解が容易になる

Virtual Learning Environment for e-Math System

In　this　paper，　I　describe　the　virtual　learning　environment　in　which　I　will　use　the　e－Math Interact　Agent　system　that　1　developed．　As　university　insrmctors，　we　require　various　instructional tools　in　our　lectures　in　addition　to　the　teaching　materials　we　have　developed　ourselves．　Two　distinguished 　virtual　learning　environment（VLE）systems，　Bodington　and　Sakal，　meet　instructor requirements　in　this　area，　Currently，　the　Tetra　pr〔）ject　is　working　to　combine　these　systems　to develop　a　next－generation　VLE　In　this　paper，　I　shall　describe　the　f¢atures　of　WebLearn　and　Tetra from　the　viewpoint　of　how　1　shall　run　and　use　my　e－Math　system　on　WebLearn　and　in　the　future on　Tetra