AUT - Farida Kachapova

Dr Farida Kachapova

Senior lecturer

Email: farida.kachapova@aut.ac.nz

Postal Address:
Private Bag 92006 Auckland 1142, New Zealand

Qualifications:

• PhD, Mathematical Logic Department, Moscow State University, Russia
• MSc with Honours, Moscow State University, Russia
• Graduate Diploma in Teaching, The University of Auckland, New Zealand
  

Memberships and Affiliations:

• Member of Association for Symbolic Logic
• Member of Australasian Association of Logic
• Member of New Zealand Mathematics Society
• An editor of Journal of Mathematics and Statistics, ISSN 1549-3644
• Member of editorial board of International Journal of Statistics and Probability, ISSN 1927-7032(Print), ISSN 1927-7040

Teaching Areas:

Calculus, differential equations, probability theory, linear and general algebra, discrete mathematics, and statistics.

Research areas:

Mathematical logic, in particular classical and intuitionistic axiomatic set theories, and proof theory;

Probability theory;

Mathematics education.

Publications:

Journal Articles

• Kashapova, F. (1984). Determination of classes of constructively derivable theorems in a many-sorted intuitionistic set theory equivalent to a second-order arithmetic. Proceedings of the USSR Academy of Sciences (Doklady Mathematics), ISSN 1064-5624. Vol. 276, Issue 4, pp.782-786.

• Kashapova, F. (1984). Constructive set theory with types, and consistency with Church's thesis. Moscow University Mathematics Bulletin, ISSN  0027-1322. Vol. 39, No. 4, pp. 1972-1975.

• Kashapova, F. (1989). Intuitionistic theory of functionals of higher type. Russian Academy of Sciences: Mathematical Notes, ISSN 0001-4346. Vol. 45, Issue 3, pp. 66-79.

• Kashapova, F. (1989) Consistency of  the formal Church’s thesis relative to a constructive set theory. Institute of Scientific and Technical Information of USSR, 35 pp. No. 1893-B 89 (23. 03. 1989).

• Kashapova, F. and Kachapov, I. (1997) Intuitionistic theory of functionals of high types. Institute of Scientific and Technical Information of USSR, 27 pp. No. 3766-B 97 (25. 12. 1997).

• Kashapova, F. (1983) Consistency of the almost predicative set theory relative to the intuitionistic theory of functionals with Cripke’s scheme. Institute of Scientific and Technical Information of USSR, 20 pp. No. 6442-83 (01. 12. 1983).

• Kashapova, F. (1983) Constructive provability of some classical theorems. Generalization of Beeson’s interpretation to an intuitionistic set theory with many sorts. Institute of Scientific and Technical Information of USSR, 40 pp. No. 5863-83 (28. 10. 1983).

• Kachapova, F. and Kachapov, I. (2005) Calculating optimal portfolios of three financial assets. Mathematics and Informatics Quarterly. Vol. 15, No. 3/4, pp. 100-107.

• Kachapova, F. and Kachapov, I. (2005) One application of analytical geometry. Mathematics and Informatics Quarterly. Vol. 15, No. 3/4, pp. 82-84.

• Kachapova, F. and Kachapov, I. (2006) The geometric and trigonometric approaches to one problem. Mathematics and Informatics Quarterly. Vol. 16, No. 3/4, pp. 69-72.

• Kachapova, F. and Kachapov, I. (2006) The substitution method in teaching mathematics. New Zealand Mathematics Magazine, ISSN 0549-0510. Vol. 43, No. 1, pp. 1-6.

• Kachapova, F., Black, M, Kachapov, I. (2007) Alternative numeral systems. Mathematics and Informatics Quarterly. Vol. 17, No. 3/4, pp. 111-115.

• Black, M,  Kachapova, F., Kachapov, I. (2007) Substitution and its applications in teaching mathematics. Mathematics and Informatics  Quarterly. Vol. 17, No. 3/4, pp. 86-93.

• Black, M., Kachapova, F., Klymchuk S., Kachapov, I. (2007) Probability counter-examples and paradoxes as a teaching strategy. Mathematics and Informatics Quarterly. Vol. 17, No. 3/4, pp. 154-160.

• Kachapova, F., Black, M, Kachapov, I. (2007) Using alternative numeral systems in teaching mathematics. Mathematics Teaching-Research Journal. Vol. 2, Issue 1, pp. 76-88. URL: www.hostos.cuny.edu/departments/math/mtrj/archives/volume2/issue1/volume2issue1full.pdf

• Kachapova, F., Black, M, Kachapov, I. (2007). Effective procedures in teaching mathematics. Mathematics Teaching-Research Journal. Vol. 2, Issue 1, pp. 89-104. URL: www.hostos.cuny.edu/departments/math/mtrj/archives/volume2/issue1/volume2issue1full.pdf

• Kachapova, F., Black, Klymchuk S., M, Kachapov, I. (2007) Counter-examples and paradoxes in teaching mathematical statistics. Mathematics Teaching-Research Journal. Vol. 2, Issue 1, pp. 105-115. URL: www.hostos.cuny.edu/departments/math/mtrj/archives/volume2/issue1/volume2issue1full.pdf

• Kachapova, F., Kachapov, I. (2008) Monotone covariance of finite samples. Mathematics and Informatics Quarterly. Vol. 18, No. 3/4, pp. 81-91.

• Kachapova, F., Kachapov, I. (2008) Algebraic approach to random variables. Mathematics and Informatics Quarterly. Vol. 18, No. 1/2, pp. 20-24.

• Kachapova, F., Kachapov, I. (2008) Geometrical approach to random variables. Mathematics Teaching-Research Journal. Vol. 2, No. 3, pp. 41-47. URL: http://www.hostos.cuny.edu/departments/math/mtrj/archives/volume2/issue3/sec4.pdf

• Kachapova, F., Kachapov, I. (2009) Review of logical paradoxes. Mathematics and Informatics Quarterly. Vol. 19, No. 1/2, pp. 9-12.

• Kachapova, F., Kachapov, I. (2010) Measuring monotony in two-dimensional samples. International Journal of Mathematical Education in Science and Technology, Vol. 41, Issue 3, pp. 418-427. URL: http://www.tandfonline.com/doi/abs/10.1080/00207390903477418        

• Kachapova, F., Kachapov, I. (2010) Orthogonal projection in teaching regression and financial mathematics. Journal of Statistics Education (JSE).  Vol. 18, No. 1, pp. 1-18. URL: http://www.amstat.org/publications/jse/v18n1/kachapova.pdf

• Kachapova, F., Kachapov, I. (2011). Students’ misconceptions about random variables. International Journal of Mathematical Education in Science and Technology, pp. 1-9. URL: http://dx.doi.org/10.1080/0020739X.2011.644332

• Kachapova, F., Kachapov, I. (2011). Percentage problems in bridging courses. International Journal of Mathematical Education in Science and Technology, pp. 1-10. URL: http://dx.doi.org/10.1080/0020739X.2011.618554

• Kachapova, F., Kachapov, I. (2011). Applying change of variable to calculus problems. International Journal of Mathematical Education in Science and Technology, Vol. 42, Issue 3, pp. 388-396. URL: http://dx.doi.org/10.1080/0020739X.2010.526251

• Klymchuk, S., Kachapova, F. (2011). Paradoxes and counterexamples in teaching and learning of probability at university. International Journal of Mathematical Education in Science and Technology, pp. 1-9. URL: www.tandfonline.com/doi/abs/10.1080/0020739X.2011.633631

• Kachapova, F. (2011) Teaching percentages through the table method. Mathematics Teaching-Research Journal. Vol. 5, No. 1, pp. 32-49. URL: www.hostos.cuny.edu/departments/math/MTRJ/archives/volume5/issue1/2_Teaching%20percentages.pdf

• Klymchuk, S., Kachapova, F., Schott, D., Sauerbier, G.,  Kachapov, I. (2011). Using paradoxes and counterexamples in teaching probability: a parallel study. Mathematics Teaching-Research Journal. Vol. 5, No. 1, pp. 50-70. URL: www.hostos.cuny.edu/departments/math/MTRJ/archives/volume5/issue1/3_Using%20Paradoxes.pdf

Conference Proceedings

• Kashapova, F. (1982) Generalization of non-type variant of Godel interpretation. Proceedings of the 6-th USSR conference on mathematical logic, p. 78. Tbilisi, USSR.

• Kashapova, F. (1986) Construction of classes of constructively derivable theorems. Proceedings of the 8-th USSR conference on mathematical logic, p. 82. Moscow, Russia.

• Kashapova, F. (1988) Three subsystems of the simple theory of types. Proceedings of the 9-th USSR conference on mathematical logic, p. 73. Leningrad,  Russia.

• Kashapova, F. and Kashapov, I. (1997) Constructive axiomatic set theory with types.  Algebra and Analysis. Proceedings of the international conference in honour of 100-th anniversary of B.M.Gagaev, pp.113-114. Kazan, Russia.

• Black, M., Kachapova, F., Kachapov, I. (2007) Improving procedures for effective teaching. Proceedings of the 30th annual conference of Mathematics Education Research Group of Australasia, ISBN 978-1-920846-14-5, v.2, p. 912, Hobart, Australia.

• Black, M., Kachapova, F., Klymchuk S., Kachapov, I. (2007) Using counter examples and paradoxes in teaching probability: students’ attitudes. Proceedings of the 30th annual conference of Mathematics Education Research Group of Australasia, ISBN 978-1-920846-14-5, v.2, p. 913, Hobart, Australia.

• Kachapova, F. & Kachapov, I. (2009) Geometric interpretation of optimal portfolio. Proceedings of the 3rd international Conference of Science and Mathematics Education, ISBN 967-930-017-8, pp. 272-279, Penang, Malaysia.

• Kachapova, F. & Kachapov, I. (2010) Population monotony coefficient. International Conference on Statistical Methodologies and Related Topics in conjunction with NZSA Annual Conference, p. 33, Palmerton North, New Zealand.

• Kachapova, F. (2011) The relative consistency of an intuitionistic theory with  functionals. The Twelfth Asian Logic conference, p. 31, Wellington, New Zealand.

• Kachapova, F. & Kachapov, I. (2011) Population Regression Model in University  Courses. Volcanic DELTA (8th Southern hemisphere conference on teaching and learning undergraduate mathematics and statistics), p. 441, Rotorua, New Zealand.

Book

• Kachapova, F. and Kachapov, I. (2006) Mathematical approach to portfolio analysis. Maths Ken, ISBN 0-473-11194-2.