• A measure of monotonicity of two random variables

      Kachapova, F; Kachapov, I (Science Publications, 2012)
      Problem statement: When analyzing random variables it was useful to measure the degree of their monotone dependence or compare pairs of random variables with respect to their monotonicity. Existing coefficients measure ...
    • Applying change of variable to calculus problems

      Kachapova, F; Kachapov, I (Taylor & Francis, 2011)
      The paper describes the technique of introducing a new variable in some calculus problems that helps students to master the skills of integration and evaluating limits. This technique is algorithmic and easy to apply; it ...
    • Finding the envelope and efficient frontier of financial assets

      Kachapova, F; Kachapov, I (Science Publications, 2012)
      Problem statement: One of the problems considered in financial mathematics is finding portfolios of given financial assets that minimize risk for targeted returns. The set of such portfolios is called the envelope of the ...
    • Measuring monotony in two-dimensional samples

      Kachapova, F; Kachapov, I (Taylor & Francis, 2010)
      The paper introduces a monotony coefficient as a new measure of the monotone dependence in a two-dimensional sample. Some properties of this measure are derived. In particular, it is shown that the absolute value of the ...
    • Monotonicity criteria

      Kachapova, F; Kachapov, I (World Academy of Science, Engineering and Technology (WASET), 2013)
      Monotonicity is an important type of dependence of random variables. The paper reviews the definitions of comonotonicity and counter-monotonicity, their existing criteria and introduces a new criterion for each of the two ...
    • Orthogonal projection in teaching regression and financial mathematics

      Kachapova, F; Kachapov, I (ASA Publications, 2010)
      Two improvements in teaching linear regression are suggested. The first is to include the population regression model at the beginning of the topic. The second is to use a geometric approach: to interpret the regression ...
    • Percentage problems in bridging courses

      Kachapova, F; Kachapov, I (Taylor and Francis, 2012)
      Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging ...
    • Students’ misconceptions about random variables

      Kachapova, F; Kachapov, I (Taylor & Francis, 2011)
      This article describes some misconceptions about random variables and related counter-examples, and makes suggestions about teaching initial topics on random variables in general form instead of doing it separately for ...