Dr Farida Kachapova

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Senior Lecturer

Email: farida.kachapova@aut.ac.nz

ORCID: ORCID logo https://orcid.org/0000-0001-6086-7309

Qualifications:

  • PhD, Moscow State University
  • MSc with Distinction, Moscow State University
  • Graduate Diploma in Teaching, University of Auckland

Research interests:

The following areas of Mathematical logic: Non-standard axiomatic theories and Automated formal reasoning;

Mathematical models in statistical physics.

Teaching summary:

Linear and general algebra, ordinary and partial differential equations, calculus.

Professional activities:

Appointment, affiliation, and membership

  • Member of Association for Symbolic Logic, Association for Symbolic Logic (2010 - ongoing)
  • Member of Australasian Association of Logic, Australasian Association of Logic (2010 - ongoing)
  • Member of New Zealand Mathematics Society, New Zealand Mathematics Society (2010 - ongoing)

Award, prize, fellowship, and scholarship

  • Celebrating 15 years of service, Auckland University of Technology (2019)
  • Award for Excellence in Learning and Teaching, Faculty of Design and Creative Technologies, Auckland University of Technology (2012)

Editorship, reviewing, examining, and judging

  • Invited reviewer, The European Physical Journal Plus (2019 - ongoing)
  • Invited Reviewer for Mathematical Reviews of American Mathematical Society (MathSciNet)., American Mathematical Society (2016 - ongoing)
  • An editor of Journal of Mathematics and Statistics, Journal of Mathematics and Statistics, ISSN 1549-3644 (2012 - ongoing)
  • Member of editorial board of International Journal of Statistics and Probability, International Journal of Statistics and Probability (2012 - ongoing)

Research outputs:

Featured research outputs

  • Kachapova, F. (2018). Formalizing Probability Concepts in a Type Theory. Journal of Mathematics and Statistics, 14(1), 209-218. doi:10.3844/jmssp.2018.209.218

  • Kachapova, F. (2017). Metamathematical properties of a constructive multi-typed theory. Studia Logica, 105(3). doi:10.1007/s11225-016-9701-0

  • Kachapova, F. (2015). A strong multi-typed intuitionistic theory of functionals. The Journal of Symbolic Logic, 80(3). doi:10.1017/jsl.2015.21

Books

  • Kachapova, F., Kachapov, I., & Fomenko, T. (2018). High Math: General Algebra in Problems. Moscow, Russia: Urait Publishing House. Retrieved from http://www.urait.ru/catalog/411431

  • Kachapova, F. (2013). Mathematical models in portfolio analysis. Bookboon.com (Ventus Publishing ApS). Retrieved from http://bookboon.com/

Journal articles

  • Kachapova, F., & Kachapov, I. (2019). Constructing Gibbs measure in a rigorous way. Journal of Mathematics and Statistics, 15(1), 308-322. doi:10.3844/jmssp.2019.308.322

  • Kachapova, F. (2018). Formalizing Probability Concepts in a Type Theory. Journal of Mathematics and Statistics, 14(1), 209-218. doi:10.3844/jmssp.2018.209.218

  • Kachapova, F., & Kachapov, I. (2017). Interaction model in statistical mechanics. Journal of Mathematics and Statistics, 13(4). doi:10.3844/jmssp.2017.339.346

  • Kachapova, F. (2017). Metamathematical properties of a constructive multi-typed theory. Studia Logica, 105(3). doi:10.1007/s11225-016-9701-0

  • Kachapova, F. (2016). Comparison of mathematical models of fibrosis. Comment on "Towards a unified approach in the modeling of fibrosis: A review with research perspectives" by Martine Ben Amar and Carlo Bianca. Physics of Life Reviews. doi:10.1016/j.plrev.2016.05.007

  • Kachapova, F. (2016). A multi-sorted version of second order arithmetic. The Australasian Journal of Logic, 13(5). Retrieved from https://ojs.victoria.ac.nz/ajl/article/view/3936

  • Kachapova, F., & Kachapov, I. (2016). Convergence of renormalization group transformations of Gibbs random field. Journal of Mathematics and Statistics, 12(3). doi:10.3844/jmssp.2016.135.151

  • Kachapova, F. (2015). Interpretation of constructive multi-typed theory in the theory of arithmetical truth. Lobachevskii Journal of Mathematics, 36(4). doi:10.1134/S1995080215040034

  • Kachapova, F. (2015). A strong multi-typed intuitionistic theory of functionals. The Journal of Symbolic Logic, 80(3). doi:10.1017/jsl.2015.21

  • Kachapova, F. (2014). On the Importance of Pure Mathematics. Invited editorial. Journal of Mathematics and Statistics, 10(4). doi:10.3844/jmssp.2014.421.422

  • Kachapova, F. (2013). Representing Markov chains with transition diagrams. Journal of Mathematics and Statistics, 9(3). doi:10.3844/jmssp.2013.149.154

  • Kachapova, F., & Kachapov, I. (2012). Students' misconceptions about random variables. International Journal of Mathematical Education in Science and Technology, 43(7). doi:10.1080/0020739X.2011.644332

  • Kachapova, F., & Kachapov, I. (2012). Finding the envelope and efficient frontier of financial assets. Journal of Mathematics and Statistics, 8(3). doi:10.3844/jmssp.2012.323.329

  • Kachapova, F., & Kachapov, I. (2012). A measure of monotonicity of two random variables. Journal of Mathematics and Statistics, 8(2). doi:10.3844/jmssp.2012.221.228

  • Kachapova, F., & Kachapov, I. (2011). Applying change of variable to calculus problems. International Journal of Mathematical Education in Science and Technology. doi:10.1080/0020739X.2010.526251

  • Kachapova, F., & Kachapov, I. (2010). Orthogonal Projection in Teaching Regression and Financial Mathematics. Journal of Statistics Education, 18(1). Retrieved from http://www.amstat.org/publications/jse/v18n1/kachapova.pdf

  • Kachapova, F., & Kachapov, I. (2010). Measuring monotony in two-dimensional samples. International Journal of Mathematical Education in Science and Technology, 41(3). doi:10.1080/00207390903477418

  • Kashapova, F. (1989). Intuitionistic theory of functionals of higher type. Russian Academy of Sciences: Mathematical Notes, 45(3). doi:10.1007/BF01158558

  • Kashapova, F. (1984). Determination of classes of constructively derivable theorems in a many-sorted intuitionistic set theory equivalent to a second-order arithmetic. Doklady Mathematics, 276(4).

Conference contributions

  • Kachapova, F. (2019). Convergence theorems in an equilibrium interaction model. In StatPhys27. Buenos Aires. Retrieved from https://statphys27.df.uba.ar/

  • Kachapova, F. (2018). Mathematical modelling of interaction in fluids and gases. In Statistical Mechanics of Soft Matter. Auckland. Retrieved from http://smsq.github.io/2018/index.html

  • Kachapova, F., & Kachapov, I. (2017). Analysis of Gibbs random field using semi-invariants. In Applied Probability @ The Rock, An international workshop celebrating Phil Pollett's 60th birthday. Ayers Rock. Retrieved from http://www.maths.adelaide.edu.au/APatR/abs%20-%20FK2.pdf

  • Kachapova, F. (2015). Modelling choice sequences of high types. In Handbook of the 5th World Congress and School on Universal Logic (pp. 333). Istanbul: Publications of Turkish Logic Society. Retrieved from http://www.uni-log.org/start5.html

  • Kachapova, F., & Kachapov, I. (2015). Limiting distribution of random field in Ising model under renorm-group transformation. In 18th INFORMS Applied Probability Society Conference: Abstract Book (pp. 143). Istanbul. Retrieved from http://home.ku.edu.tr/~aps2015/images/program/abstract%20book.pdf

  • Kachapova, F. (2015). Realizability and existence property of a constructive set
    theory with types. In Proceedings of the 13th Asian Logic Conference (pp. 136-155). Guangzhou: World Scientific. doi:10.1142/9789814678001_0009

  • Kachapova, F., & Kachapov, I. (2014). Convergence of random field transformed by renormalization group. In AUT Mathematical Sciences Symposium (pp. 15). Auckland. Retrieved from http://www.aut.ac.nz/

  • Kachapova, F. (2014). Properties of an intuitionistic multi-typed theory with operations. In Algebra and Mathematical Logic: Theory and Applications (pp. 66). Kazan. Retrieved from http://kpfu.ru/portal/docs/F344663063/__Main.pdf

  • Kachapova, F. (2013). A Beth model with infinitely many types of functionals. In The 13th Asian Logic conference (pp. 18). Guangzhou. Retrieved from http://logic.sysu.edu.cn/alc2013/ALC2013-program.pdf

  • Kachapova, F. (2013). A generalization of Beth model to functionals of high types. In Proceedings of the 12th Asian Logic Conference (pp. 185-209). Wellington: World Scientific. doi:10.1142/9789814449274_0011

  • Kachapova, F. (2012). A Beth model for intuitionistic functionals with types. In AAL 2012 Timetable and Abstracts (pp. 12-13). Sydney. Retrieved from http://www.personal.usyd.edu.au/~njjsmith/aal2012/aal2012.pdf

  • Kachapova, F. (2011). The relative consistency of an intuitionistic theory with functionals. In The 12th Asian Logic conference (pp. 31). Wellington.

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

  • Kachapova, F., & Kachapov, I. (2009). Geometric Interpretation of Optimal Portfolio. In 3rd International Conference of Science and Mathematics Education (CoSMEd) (pp. 272-279). Penang.

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