Prof. Risto Malcheski, PhD Faculty of Communication and IT

  • Function: Vice-chancelor
  • Subjects:
  • Education:

Prof. Risto Malcheski, Ph.D.

 

Education:

Ph.D. in mathematical science, Faculty of Natural Science and Mathematics, Ss. Cyril and Methodius University, Skopje

M.Sc. in mathematical science, Faculty of Natural Science and Mathematics, Ss. Cyril and Methodius University, Skopje

Engineer in Applied Mathematics, Mathematics Faculty, Ss. Cyril and Methodius University, Skopje

Mathematical Gymnasium Georgi Dimitrov, Skopje

 

Scientific fields:

А)     Functional Analysis

Б)      Methodology of Teaching Mathematics

 

Current teaching assignment:

  • Algebraic Structures,
  • Probability and Statistics,
  • Discrete Mathematics,
  • Calculus 1,
  • Calculus 2,
  • Mathematics for Business,
  • Methodology of scientific research,
  • Selected chapters of mathematical analysis,
  • Operations Research, and
  • Statistics for Business.  

 

Some previous managerial functions:

  • Vice-Rector for teaching at FON University, Skopje
  • Vice-Rector for teaching at European University, Skopje
  • President of Union of mathematicians of Macedonia
  • President of the Union of mathematicians and computer scientists of Macedonia
  • Vice-president of Society of mathematicians and computer scientists of Skopje
  • Chief Editor of mathematical journal SIGMA, Skopje
  • Chief Editor of mathematical journal NUMERUS, Skopje
  • President of the Commission for publishing activity at Faculty of natural science and mathematics, Ss. Cyril and Methodius University, Skopje
  • The President of Publishing Council at Faculty of natural science and mathematics, Ss. Cyril and Methodius University, Skopje
  • Head of the Office of Applied Mathematics, Institute of Mathematics at Faculty of natural science and mathematics, Ss. Cyril and Methodius University, Skopje

 

Other activities in the profession:

  • reviewer of Math Reviews
  • participation on twenty math symposiums and conferences, both national as well as international character,
  • held more cycles lectures on statistics and actuarial mathematics for training of actuaries and brokers at the Ministry of Finance,
  • repeatedly leader and deputy leader of the Macedonian representations on Balkan and International Mathematical Olympiads for students of primary and secondary education,
  • organization and participation in professional and scientific bodies on two congresses of Union of Mathematicians of Macedonia and a Congress MASSEE,
  • organization and participation in professional bodies on two Balkan Olympiads for high school students (1999 and 2008) and two Balkan Olympiads for students from elementary school (2000 and 2014), and
  • President of the Commission for the proficiency (state) exam for teachers of secondary mathematics education at the Ministry of Education and Science,

 

Projects participations

1993-1995  Mathematical models, methods and procedures in the optimization of the production and technical problems, Faculty of Mechanical Engineering, Skopje

2000-2002  Methods on Applied Functional Analysis, Faculty of natural science and mathematics, Skopje

2009           Edubuntu, Ministry of Education and Science, Ministry of Information Society, training over 4,500 teachers in secondary education on educational technology topic (Edubuntu),

2010           Modernization of education, Ministry of Education and Science, training on over 2100 teachers in primary education

2010-2013  “DL@WEB - Enhancing the quality of distance learning at Western Balkan higher education institutions“, TEMPUS, University of Kragujevac, Serbia, 2010-2013

2010-2012  “iKNOW – Innovation and Knowledge Management, eStudent Information System”, TEMPUS, LSBU London, United Kingdom, 2010-2013,

 

Publications 

 

A)   University books

  1. Dimovski, D., Trenchevski, K., MalcheskiR., Josifovski, B. (1993). Practiced the elementary mathematics, Prosvetno delo, Skopje
  2. MalcheskiR. (2001). Fundamentals of mathematical analysis, Ss. Cyril and Methodius University, Skopje
  3. MalcheskiR. (2002). Mathematical analysis I, Faculty of natural science and mathematics, Skopje
  4. MalcheskiR. (2010). Methodology of teaching arithmetic and algebra in elementary school, FON University, Skopje
  5. MalcheskiR. (2010). Methodology of teaching mathematics (Second Edition), FON University, Skopje
  6. MalcheskiR. (2013). Mathematical analysis II, FON University, Skopje
  7. MalcheskiR., Malcheska, V. (2010). Probability theory, FON University, Skopje
  8. MalcheskiR., Malcheska, V. (2011). Mathematics 3 - Calculus 1 (third edition), FON University, Skopje
  9. MalcheskiR., Malcheska, V. (2011). Mathematics 4 - Calculus 2 (third edition), FON University, Skopje
  10. MalcheskiR., Malcheska, V. (2011): Mathematics 5 – Discrete mathematics (second edition), FON University, Skopje
  11. MalcheskiR., Malcheska, V. (2012). Mathematics 1 – Algebraic structures (second edition), FON University, Skopje
  12. MalcheskiR., Malcheska, V. (2012). Mathematics 2 – Vector and linear algebra (second edition), FON University, Skopje
  13. MalcheskiR., Malcheski, S. (2010). Basics of Financial Mathematics, ALFA 94, Skopje
  14. MalcheskiR., Malcheski, S. (2010). Mathematics for business (fourth edition), FON University, Skopje
  15. MalcheskiR., Malcheski, S. (2010). Statistics for business (fourth edition), FON University, Skopje
  16. MalcheskiR., Malcheski, S. (2015). Operations Research, FON University, Skopje
  17. MalcheskiR., Malcheski, S., Anevska, K. (2014). Methodology of scientific and research work, FON University, Skopje

 

B)   Books for secondary and primary education

  1. MalcheskiR. (2002). Elementary algebra, Prosvetno delo, Skopje
  2. MalcheskiR. (2008). Mathematics for second grade (authorized manuscript),
  3. MalcheskiR. (2008). Mathematics for third grade, Tabernakul, Skopje
  4. MalcheskiR. (2008). Mathematics worksheets for third grade, Tabernakul, Skopje
  5. MalcheskiR., Dokoska, M. (2002): Mathematics 2, Prosvetno delo, Skopje
  6. Trenchevski, G., MalcheskiR., Trenchevski, K. (2003). Mathematics 3, (authorized manuscript)

 

C)   Thematic books for working with talented students

  1. MalcheskiR., Malcheski, А. (1993). Selected contents of elementary mathematics, SMM, Skopje
  2. MalcheskiR., Dimovski, D., Trencevski, K. (1993). Introduction to number theory, МММ, Skopje
  3. Trencevski, К., MalcheskiR., Dimovski, D. (1994). Interesting mathematics, MMM, Skopje
  4. MalcheskiR., Malcheski, A. (2000). For the youngest mathematitions, SMM, Skopje
  5. MalcheskiR. (2014). Inequalities, Skopje
  6. MalcheskiR. (2014). Functions and functional equations, Skopje
  7. MalcheskiR., Malcheski, А., Anevska, К. (2014). Introduction to elementary number theory, SMM, Skopje
  8. MalcheskiR., Malcheski, A., Anevska, K. (2014). Solving word problems (third edition), SMM, Skopje
  9. Piperevski, B., MalcheskiR., Malcheski, А., Trajkovska I. (2001). Selected contents of elementary mathematics II, Sigma, Skopje
  10. MalcheskiR., Malcheski, А., Anevska, К., Manova-Erakovikj, V., Markoski, Gj., Stojkovska, I. (2015). Selected problems from elementary algebra (third edition), SMM, Skopje
  11. MalcheskiR., Malcheski, A., Anevska, K. (2015). Following the paths of champions in mathematics, SMM, Skopje
  12. MalcheskiR., Grozdev, S., Anevska, K. (2015). Geometry of a complex number, Arhimed, Sofia

 

D)   Volumes of problems from competitions

  1. MalcheskiR. and others. (1995). Mathematics Competitions '94, SMM, Skopje
  2. MalcheskiR. and others. (1996). Mathematics Competitions '95, SMM, Skopje
  3. MalcheskiR. and others. (1997). Mathematics Competitions '96, SMM, Skopje
  4. MalcheskiR., Dimovski, D., Jakimovik, S., Malcheski, А. (2001). Autumn mathematical tournament Crnorizec Hrabar, SMM, Skopje
  5. MalcheskiR., Dimovski, D., Malcheski, А., Manova – Erakovik, V. (2000). International mathematical olympiads, SMM, Skopje
  6. Malcheski, А., MalcheskiR. and others. (2000). Mathematics contests in secondary education in 1998-99, SMM, Skopje
  7. MalcheskiR., Manova – Erakovik, V., Markovski, Gj., Malcheski, А. (2008). Sigma treasury (section problems 1-505), SMM, Skopje
  8. Malcheski, А., Manova – Erakovik, V., MalcheskiR. (2011). Regional competitions in mathematics 1974 - 2011, SMM, Skopje
  9. Malcheski, А., Manova – Erakovik, V., MalcheskiR. (2011). Sigma treasury (section preparatory problems), SMM, Skopje
  10. Malcheski, А., Manova – Erakovik, V., MalcheskiR. (2011). Sigma treasury (competitive problems 1-144), SMM, Skopje
  11. Malcheski, А., Manova – Erakovik, V., MalcheskiR. (2011). Sigma treasury (section problems 1006-1200), SMM, Skopje
  12. Malcheski, А., Manova – Erakovik, V., MalcheskiR. (2011). Sigma treasury (section problems 506-1005), SMM, Skopje
  13. Malcheski, А., Manova – Erakovik, V., MalcheskiR. и др. (2014). Contests in mathematics 2006-2013 (Primary Education), SMM, Skopje

 

E)   Other books

  1. Dimoski, I., MalcheskiR., Malcheska, C. (2010). Monitoring, verification and evaluation of students' achievements, FON University, Skopje
  2. MalcheskiR., Malcheska, C. (2010). Working with talented students, FON University, Skopje
  3. MalcheskiR., Malcheska, C. Malcheska, F. (2010). Strategies and techniques of learning and teaching, FON University, Skopje

 

F)    Papers on functional analysis

  1. Trenchevski, K., MalcheskiR. (1994). On the Transformation in the Operational Calculus, Annual Review of the Institute of Mathematics, 35
  2. MalcheskiR. (1996). Remarks on n-normed spaces, Mathematical Bulletin, 20
  3. MalcheskiR. (1996): Remarks on n-normed spaces, Proceedings from I congress of mathematicians and computer scientists of Macedonia, Ohrid
  4. Malcheski, А., MalcheskiR. (1997). L1(μ) as a n-normed spaces, Annual Review of the Institute of Mathematics, 38
  5. Malcheski, А., MalcheskiR. (1997). n-seminormed spaces, Annual Review of the Institute of Mathematics, 38
  6. MalcheskiR. (1997). Strong convex n-normed spaces, Contributions, Sec. Mat. Tech. Sci., MANU. XVIII, 1-2
  7. MalcheskiR. (1997). Strong n-convex n-normed spaces, Mathematical Bulletin, 21, 
  8. MalcheskiR. (1999). The Hahn-Banach theorem for bounded n-linear functionals, Mathematical Bulletin, 23
  9. Malcheski, А., MalcheskiR. (2000). Remarks on n-seminormed space, Proceedings from II congress of mathematicians and computer scientists of Macedonia, Ohrid
  10. Malcheski, А., MalcheskiR. (2000). Convergent sequences in n-normed spaces, Mathematical Bulletin, 24
  11. MalcheskiR., Malcheski, А. (2000). n- Banach spaces, Proceedings from II congress of mathematicians and computer scientists of Macedonia, Ohrid  
  12. MalcheskiR. (2001). n- semi scalar product with characteristic p, Mathematical Bulletin, 25
  13. MalcheskiR. (2003). Gateauxs inference on n-normed, Mathematical Bulletin, 27
  14. MalcheskiR. (2004). Generalized n- scalar product, Conference proceedings, VII symposium on differential equations, Ohrid
  15. MalcheskiR. (2004). Theorem of Ascoli-Mazur in n-normed space, Mathematical Bulletin, 28
  16. Malcheski, А., MalcheskiR. (2005). Lp(μ) as 2-normed spaces, Mathematical Bulletin, 29
  17. Calamani, S., MalcheskiR. (2005). Continuous linear n- functionals, Proceedings from III congress of mathematicians of Macedonia, Struga
  18. Trenchevski, K., MalcheskiR. (2006). n-iner product and its applications, Journal of Inequalities in Pure and Applied mathematics, Volume 7, Issue 2
  19. MalcheskiR., Cvetkovski, Z. (2012). Dual space of the space of bounded linear n-functionals, Matematicki bilten, 36
  20. Anevska, K., MalcheskiR. (2014). Characterization of 2-inner product using Euler-Lagrange type of equality, International Journal of Science and Research (IJSR), ISSN 2319-7064, Vol. 3 Iss. 6, pp. 1220-1222
  21. Anevska, K., MalcheskiR. (2014). Generalization on parallelepiped equality in 2-normed space, IJPAST, ISSN 2229 - 6107, Vol. 22 No. 2, pp. 41-49
  22. Anevska, K., MalcheskiR. (2014). Remarks on one S. S. Dragomir’s results, American journal of Engineering Research, (AJER), e-ISSN 2320-0847 p-ISSN  2320-0936, Vol. 03, Iss. 02, pp. 1-3
  23. MalcheskiR., Anevska, K. (2014). About the 2-Banach spaces, International Journal of Modern Engineering Research (IJMER), ISSN 2249–6645, Vol. 4  Iss. 5, pp. 28-32
  24. MalcheskiR., Anevska, K. (2014). Characterization of 2-inner product by strictly convex 2-norm of modul c, International Journal of Mathematical Analysis, Vol. 8, No. 33, pp. 1647-1652, HIKARI Ltd, www.m-hikari.com
  25. MalcheskiR., Anevska, K. (2014). Families of norms generated by 2-norm, AJER, e-ISSN  2320-0847 p-ISSN  2320-0936, Vol. 03, Iss. 05, pp. 315-320
  26. MalcheskiR., Nasteski, Lj., Nachevska, B., Huseini, A. (2014) - About the strictly convex and uniformly convex normed and 2-normed spaces., IJSIMR, e-ISSN 2347-3142, p-ISSN 2346-304X, Vol. 2, Iss. 06, pp. 603-610
  27. Malcheski, R., Anevska, K. (2014). Strictly convex in quasi 2-pre-Hilbert space, IJSIMR, e-ISSN 2347-3142, p-ISSN 2346-304X, Vol. 2, Iss. 07, pp. 668-674
  28. MalcheskiR. (2014). Inequality among the inner products of three vectors into the real Hilbert space, International Journal of Mathematical Analysis, Vol. 8, No. 47, pp. 2319 - 2323, HIKARI Ltd, www.m-hikari.com
  29. MalcheskiR., Anevska, K. (2014). Parallelepiped inequality into 2-normed space and its consequencies, IJSIMR, e-ISSN 2347-3142, p-ISSN 2346-304X, Vol. 2, Iss. 08, pp. 719-728
  30. Malcheski, S., Malcheski, R., Anevska, K. (2014). 2-semi-norms and 2*-semi-inner product, Hikari, International Journal of Mathematical Analysis, Vol. *, No. **, pp. **** - ****, HIKARI Ltd, www.m-hikari.com (прифатен за печат)
  31. Malcheski, R., Malceski, A. (2015). Inequalities of Dunkl-Williams and Mercer type in Quasi-Normed Space, IJSIMR, e-ISSN 2347-3142, p-ISSN 2346-304X, Vol. 3, Issue 1, pp. 67-70
  32. Malcheski, R. (2015). Inequalities of Pecaric-Rajic type in quasi-normed space, Applied Mathematical Sciences, Vol. 9, no. 15, 729-737
  33. Malceski, S., Malceski, A., Anevska, K., Malcheski, R. (2015). Another characterization’s of 2-pre-Hilbert Space, IJSIMR, e-ISSN 2347-3142, p-ISSN 2346-304X, Vol. 3, Issue 2, pp. 45-54
  34. Malcheski, R. (2015). Sharp Triangle Inequalities in Quasi-Normed Spaces, British Journal of Mathematics & Computer Science, Vol. 7 No. 4, pp. 258-265
  35. Malceski, A. , Malcheski, R., Anevska, K., Malceski, S. (2015). A remark about quasi 2-normed space, Applied Mathematical Sciences, Vol. 9, no. 55, 2717-2727
  36. Malceski, A., Malcheski, R. (2015). Inequalities of Pecaric-Rajic type in quasi 2-normed space, no. IJSIMR, e-ISSN 2347-3142, p-ISSN 2346-304X, Vol. 3, Issue 5, pp. 1-7

 

G)   Papers on teaching methodology

  1. MalcheskiR., Malcheska, C., Trenchevski, K., Stojoski, S. (1994). Some knowledge facts of the correlation of curricula in math – naturally area in the teaching from V to VIII grade of primary education Proceedings of Symposium, Oteshevo
  2. MalcheskiR. (1996). Qualifying exams in mathematics for university, Proceedings from I congress of mathematicians and computer scientists of Macedonia, Ohrid
  3. MalcheskiR. (1996). Mathematics exams for secondary school enrollment, Proceedings from I congress of mathematicians and computer scientists of Macedonia, Ohrid
  4. MalcheskiR., Malcheski, А. (1997): Development of talented students in mathematics, Obrazovni refleksi, 3-4, Skopje, 
  5. Malcheska, C., MalcheskiR. (1997). Ability of the teacher to successful monitoring, checking and evaluation of students' achievements, International symposium on assessing, BRO, Skopje
  6. Malcheska, C., MalcheskiR. (1999). Educational Crossroads on the threshold of XXI century, Prosvetno Delo, Skopje
  7. MalcheskiR., Malcheski, А., Trajkovska, I. (2000): Complex numbers, the possibility of internal integration course in mathematics, Proceedings from II congress of mathematicians and computer scientists of Macedonia, Ohrid
  8. MalcheskiR. (2003). Methodological note on introducing of the notion irrational number, Prosvetno delo, 2
  9. MalcheskiR., Gogovska, V. (2003). Using means inequality form getting structural mathematical knowledge, The Third International Conference “creativity in Mathematics Education end the Education of Gifted Students”, Ruse, Bugaria
  10. MalcheskiR., Gogovska, V. (2004). The Role of Educational method in teaching of gifted and talented students, The 10th International Congress on Mathematical Education,  Copenhagen, Denmark
  11. Gogovska, V., MalcheskiR. (2005). Generalization – Challenge for Gitfed Students, Procee­dings of the Tenth International Seminar of Mathematical Education on Creativity Developmnet, Daejeon, Korea, 
  12. Govovska, V., MalcheskiR. (2005). The proof in the mathematical classroom, International Conference, Mainz, Germany  
  13. MalcheskiR., Govovska, V.  (2005). Integration of teaching, the challenge of modern teaching Mathematics, Proceedings from III congress of mathematicians of Macedonia, Struga
  14. MalcheskiR., Govovska, V.  (2005). The role of methods of learning and teaching mathematics, International koferencija Svishtov, Bulgaria
  15. Gogovska, V., MalcheskiR. (2008). Counter-examples in lecturing mathematics, Proceedings of the 11th International Congress on Mathematical Education, Monterrey, Mexico
  16. Gogovska, V., MalcheskiR. (2009). Discovering errors while solving mathematical tasks, Proceedings Education of the 3th International Congress on Mathematics MICOM 2009, Ohrid, Macedonia
  17. Gogovska, V., MalcheskiR. (2010). Introducing textual tasks in mathematics curriculum, Shumen, Bulgaria
  18. Gogovska, V., MalcheskiR. (2011). Mathematical models in mathematics curriculum, Riga, Latvia
  19. Gogovska, V., MalcheskiR. (2012). Improvement intra-disciplinary integration of mathematics instruction, Elsevier, Procedia - Social and Behavioral Sciences, 46, 5420-5424
  20. Gogovska, V., MalcheskiR. (2012). The creative teacher, factor for improving mathematics instruction, Proceedings of the 7-th MCG Conference, Busan, Korea  
  21. Glavche, M., MalcheskiR. (2012). Omissions in Mathematical Knowledge of Students in Primary Education. Proceedings of 1th International Scientific Conference „Education in the Modern European Environment“, Opatija,
  22. Glavche, M., MalcheskiR. (2013). Errors in the mathematical education made by the students from the second grade, Ucitel, Bitola
  23. Glavche, M., MalcheskiR. (2013). Errors in the mathematics education made by third grade students, Conference Proceedings of International Conference “Innovations, Challenges and Tendencies in the Post Modern Education”, Stara Zagora
  24. Glavche, M., MalcheskiR. (2013). The type of mathematical errors made by the students in the elementary education, Journal of Pedagogy, Skopje
  25. Anevska, K., Gogovska, V., MalcheskiR. (2014).  The role of complex numbers in interdisciplinary integration in mathematics teaching, Elsevier, Procedia - Social and Behavioral Sciences
  26. Glavche, M., Anevska, K., MalcheskiR. (2014). Learning the methodology of mathematical problem solving in elementary education, IJSR, ISSN 2319-7064, Vol. 3, Iss. 9, pp. 809-813
  27. Gogovska, V., Anevska, K., MalcheskiR. (2014) - Properties of Thinking and Adoption of Mathematical Knowledge, Proceedings of the 2014 International Conference on Education and Educational Technologies II (EET '14), Praga
  28. MalcheskiR. (2014). Honeycomg - a Genius Creation of Nature, Mathematics and Informatics, Vol. 57, No. 4, pp. 402-407
  29. MalcheskiR., Anevska, K., Glavche, M. (2014). The integration of  mathematics instruction in elementary education, IJSR, ISSN 2319-7064, Vol. 3, Iss. 9, pp. 2394-2398
  30. MalcheskiR., Gogovska, V., Anevska, K. (2014). Algebraic rational expressions in mathematics, IJSR, Vol. 3 Issue 10, pp.
  31. Glavche, M., MalcheskiR., Anevska, K. (2015). Errors in the mathematical education made by the students from the fifth grade I, (прифатен за печат)
  32. Glavche, M., MalcheskiR., Anevska, K. (2015). Errors in the mathematical education made by the students from the fifth grade II, (прифатен за печат)

 

H)   Other scientific papers

  1. Стојаноски, З., MalcheskiR (1983). Game theory, Annual of Faculty of Economics, Prilep
  2. MalcheskiR. (1986). Objectively determining the type of function of the trend in economic processes, Annual of Faculty of Economics, Prilep
  3. MalcheskiR., Malcheski, А. (1995). Modification of the method of Hook Dzhivs for solving tasks of nonlinear programming, paper to the project “Mathematical models, methods and procedures in the optimization of the production and technical problems”, 71-85
  4. MalcheskiR., Malcheski, S., Stojchevska, Т. (2009). Planning for supply and Consumption of Spare, Visione, Skopje
  5. MalcheskiR., Malcheski, S., Stojchevska, Т. (2009). Methods for correcting errors in the data time series, Visione, Skopje
  6. MalcheskiR., Malcheski, S. (2012). The structure of higher education, a prerequisite for the development of knowledge-based economy, Proceedings of the scientific conference of Institute for Economy, Skopje, 30.05.2012
  7. Anevska, K., MalcheskiR. (2014). Information reliability into in automated system of managing, IJCER, ISSN (e) 2250 – 3005, Vol. 04 Issue 7, pp. 46-50

 

  1. )    Specialized papers
  1. MalcheskiR. (1992). The rational roots of a polynomial from n degree with integer coefficients, Sigma, Skopje
  2. MalcheskiR. (1993). Elementary examination on course and sketching the graph of cubic function, Sigma, Skopje
  3. MalcheskiR. (1994). Math games 1, Numerus, Skopje
  4. MalcheskiR. (1994). Math games 2, Numerus, Skopje
  5. MalcheskiR., Malcheski , А. (1994). Heron triangles, Sigma, Skopje
  6. MalcheskiR. (1995). Oh they Pythagoras triplets, Sigma, Skopje
  7. MalcheskiR. (1995). Math games 3, Numerus, Skopje
  8. MalcheskiR. (1995). Math games 4, Numerus, Skopje
  9. MalcheskiR. (1995). Family solving a "simple" problem, Sigma, Skopje
  10. MalcheskiR. (1995). Clockwise move, so what, Numerus, Skopje
  11. MalcheskiR. (1995). Triangular numbers, Sigma, Skopje
  12. MalcheskiR., Malcheski, А. (1995). The golden section, Numerus, Skopje
  13. MalcheskiR. (1996). Two important inequalities and the number е, Sigma, Skopje
  14. Malcheski, А., MalcheskiR. (1997). Breaking the numbers, Matematica+, Sofija
  15. MalcheskiR. (1997). How to help the fly that does not know geometry, Numerus, Skopje 
  16. MalcheskiR., Malcheski, А. (1997). Helly theorem for convex sets, Matematica+, Sofija
  17. MalcheskiR. (1998). To prove the conditional inequalities, Plus, Тетово
  18. MalcheskiR. (1999). Theorem Menelaj, Sigma, Skopje
  19. MalcheskiR. (2000). Problem of colors, Sigma, Skopje
  20. MalcheskiR., Malcheski, А. (2000). Reflecting the plane by complex numbers I, Sigma, Skopje
  21. MalcheskiR., Malcheski, А. (2000). Reflecting the plane by complex numbers II, Sigma, Skopje
  22. MalcheskiR. (2001). One task more ways of solving, Sigma, Skopje
  23. MalcheskiR. (2001). Parketiraniya and applications, Matematica +, Sofija
  24. MalcheskiR., Malcheski, А. (2001). Reflecting the plane by complex numbers III, Sigma, Skopje
  25. MalcheskiR., Malcheski, А. (2001). Reflecting the plane by complex numbers IV, Sigma, Skopje
  26. MalcheskiR. (2003). Inequalities between the middles and calculate the square root of a positive number, Matematica+, Sofija
  27. MalcheskiR. (2004). Multiplicative function and Euler theorem, Sigma, Skopje
  28. MalcheskiR. (2004). Several elementary algebraic methods for determining extreme values, Sigma, Skopje
  29. MalcheskiR. (2005). The identity of Sophie Germain, Numerus, Skopje
  30. MalcheskiR. (2005). Method of invariant 1, Numerus, Skopje
  31. MalcheskiR. (2005). Method of invariant 2, Numerus, Skopje
  32. MalcheskiR., Cvetkovski, Z. (2005). Mathematical induction 1, Sigma, Skopje
  33. MalcheskiR., Cvetkovski, Z.  (2005). Mathematical induction 2, Sigma, Skopje
  34. Cvetkovski, Z., MalcheskiR. (2006). An algorithm for generating Pitagora triples, Sigma, Skopje
  35. Cvetkovski, Z., MalcheskiR. (2007). Inequalities on Schur and Muirhead, Sigma, Skopje
  36. Cvetkovski, Z., MalcheskiR. (2008). Proving the symmetric inequalities with three variables, Sigma, Skopje
  37. Cvetkovski, Z., MalcheskiR. (2008). One method for proving inequalities with three variables, Sigma, Skopje
  38. MalcheskiR. (2009). Fibonacci numbers, Sigma, Skopje
  39. MalcheskiR. (2011). Inequalities between middles, Sigma, Skopje
  40. MalcheskiR. (2011). Inequality of Cauchy-Schwarz-Bunjakovski, Sigma, Skopje
  41. MalcheskiR. (2011). Chebyshev inequality, Sigma, Skopje
  42. Anevska, К., MalcheskiR. (2012). Congruence in the set of integers II, Numerus, Skopje
  43. MalcheskiR. (2012). King Arthur and the Round Table, Numerus, Skopje
  44. MalcheskiR. (2012). Linear Diophantine equalitie, Numerus, Skopje
  45. MalcheskiR. (2012). Inequalities between middles, Numerus, Skopje
  46. MalcheskiR., Anevska, К. (2012). Congruence in the set of integers I, Numerus, Skopje
  47. MalcheskiR. (2013). Honeycomg - a Genius Creation of Nature, Sigma, Skopje
  48. MalcheskiR. (2014). Method of invariant, Sigma, Skopje
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