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    Dr. Stephen M. Jodis, Dean
    The Herbert W. Boyer School of Natural Sciences, Mathematics, and Computing
    Phone: (724) 805-2631
    stephen.jodis@email.stvincent.edu  


Home > Majors and Programs > Mathematics
  • Dr. Michael W. Botsko

    Professor of Mathematics   

    W204, Sis and Herman Dupré Science Pavilion 

    (724) 805-2335
    mike.botsko@email.stvincent.edu  

    Office hours:
    Mon, Tues, Wed, Fri: 9:30 to 10:30
    Mon: 2:30 to 3:30

    Education

    B. S., Duquesne University 
    M. S., Duquesne University  Michael Botsko
    Ph. D., University of Pittsburgh

    Courses Taught

    MA 109/111 Calculus I
    MA 110 Calculus II
    MA 115 Linear Algebra
    MA 203 Complex Variables
    MA 204 Topology
    MA 206 Real Analysis I
    MA 207 Real Analysis II

     

    Publications

    M. W. Botsko and R. Gosser, On the Differentiability of Functions of Several Variables, The American Mathematical Monthly, 92 (1985), 663-665.

    M. W. Botsko and R. Gosser, Stronger Versions of the Fundamental Theorem of Calculus, The American Mathematical Monthly, 93 (1986), 294-296.

    M. W. Botsko, A First Derivative Test for Functions of Several Variables, The American Mathematical Monthly, 93 (1986), 558-561.

    M. W. Botsko, An Easy Generalization of the Riemann Integral, The American Mathematical Monthly, 93 (1986), 728-732.

    M. W. Botsko, A Unified Treatment of Various Theorems in Elementary Analysis, The American Mathematical Monthly, 94 (1987), 450-452.

    M. W. Botsko, An Elementary Proof that a Bounded a.e. Continuous Function is Riemann Integrable, The American Mathematical Monthly, 95 (1988), 24-252.

    M. W. Botsko, The Use of Full Covers in Real Analysis, The American Mathematical Monthly, 96 (1989), 328-333.

    *Michael W. Botsko, Jean-Pierre Grivauz, Marcin E. Kuczma, Solution to Problem E3329, The American Mathematical Monthly, 98 (1991), 267-268.

    M. W. Botsko, A Fundamental Theorem of Calculus that Applies to all Riemann Integrable Functions, Mathematics Magazine, 64 (1991), 347-348.

    M. W. Botsko, When is the Product of Two Derivatives a Derivative?, Mathematics Magazine, 65 (1992), 186-187.

    Michael W. Botsko, A Simple Proof of the Derivative of the Indefinite Riemann-Complete Integral, The Real Analysis Exchange, 28(1) (2002/2003), 215-220.

    Michael W. Botsko, An Elementary Proof of Lebesgue's Differentiation Theorem, The American Mathematical Monthly, 110 (2003), 834-838.

    Michael W. Botsko, Q943 and A943, Mathematics Magazine, 77 No. 4, (2004), 321 and 326-327.

    Michael W. Botsko, Q953 and A953, Mathematics Magazine, 78 No. 4, (2005), 324 and 328.

    Michael W. Botsko, Proposed Problem 11207, The American Mathematical Monthly, 113 (2006), 180.

    Michael W. Botsko, Q960 and A960, Mathematics Magazine, 79 No. 2, (2006), 151 and 155.

    Michael W. Botsko, Q961 and A961, Mathematics Magazine, 79 No. 3, (2006), 219 and 226.

    Michael W. Botsko, Proposed Problem 11232, The American Mathematical Monthly, 113 (2006), 567.

    Michael W. Botsko, Q966 and A966, Mathematics Magazine, 79 No. 6, (2006), to appear in December.

    Michael W. Botsko, Q966 and A966, Mathematics Magazine, 79 No. 5, (2006), 394 and 399.

    Michael W. Botsko, Solution to Problem 11166, The American Mathematical Monthly, 114 (2007), 83.

    Michael W. Botsko, Q967 and A967, Mathematics Magazine, 80 No. 1, (2007), 78 and 82.

    Michael W. Botsko, Problem 1766, Mathematics Magazine, 80 No. 2, (2007), 145.

    Michael W. Botsko, Exactly Which Bounded Darboux Functions Are Derivatives?, The American Mathematical Monthly, 114 No. 3, (2007), 242-246.

    Michael W. Botsko, Q971 and A971, Mathematics Magazine, 80 No. 3, (2007), 231 and 236.

    Michael W. Botsko, Q975 and A975, Mathematics Magazine, 80 No. 5, (2007), 393 and 398.

    Michael W. Botsko, Problem 1788, Mathematics Magazine, 81 No. 1, (2008), 63.

    Michael W. Botsko, Q977 and A977, Mathematics Magazine, 81 No. 1, (2008), 64 and 68.

    Michael W. Botsko, Q979 and A979, Mathematics Magazine, 81 No. 2, (2008), 156 and 161.

    Michael W. Botsko, Q982 and A982, Mathematics Magazine, 81 No. 3, (2008), 221 and 226.

    Michael W. Botsko, Problem 2003, Mathematics Magazine, 81 No. 4, (2008), 304.

    Michael W. Botsko, Q990 and A990, Mathematics Magazine, 82 No. 2, (2009), 148 and 152.

    Michael W. Botsko, Q991 and A991, Mathematics Magazine, 82 No. 3, (2009), 228 and 232.

    Michael W. Botsko, Q993 and A993, Mathematics Magazine, 82 No. 4, (2009), 311 and 316.

    Michael W. Botsko, Q996 and A996, Mathematics Magazine, 82 No. 5, (2009), 383 and 390.

    Michael W. Botsko, Q1000 and A1000, Mathematics Magazine, 83 No. 2, (2010), 150 and 153.

    Michael W. Botsko, Q1002 and A1002, Mathematics Magazine, 83 No. 3, (2010), 227 and 233.

    Michael W. Botsko, Problem 1853 , Mathematics Magazine, 83 No. 4, (2010), 303.

    Michael W. Botsko, Q1005 and A1005, Mathematics Magazine, 83 No. 5, (2010), 392 and 397.

    Michael W. Botsko, Q1010 and A1010, Mathematics Magazine, 84 No. 2, (2011), 151 and 156, 157.

    Michael W. Botsko, Solution to Problem 1850, Mathematics Magazine, 84 No. 3, (2011), 235, 236.

    Michael W. Botsko, Q1015 and A1015, Mathematics Magazine, 84 No. 5, (2011), 387 and 393.

    Michael W. Botsko, Q1019 and A1019, Mathematics Magazine, 85 No. 2, (2012), 151 and 157.

    Michael W. Botsko, Problem 1894, Mathematics Magazine, 85 No. 2, (2012), 152.

    Michael W. Botsko, Q1021 and A1021, Mathematics Magazine, 85 No. 3, (2012), 229 and 235. 

    Michael W. Botsko, Solution to Problem 11555, The American Mathematical Monthly, 119 (2012), 704 and 705.

    Michael W. Botsko, Q1025 and A1025, Mathematics Magazine, 85 No. 5, (2012), 385 and 391.

    Michael W. Botsko, Problem 1914, Mathematics Magazine, 86 No. 1, (2013), 64.

    Michael W. Botsko, Q1032 and A1032, Mathematics Magazine, 86 No. 3, (2013), 228 and 234.

    Michael W. Botsko, Q1036 and A1036, Mathematics Magazine, 86 No. 5, (2013), 382 and 387.

    Michael W. Botsko, Problem 1940, Mathematics Magazine, 87 No. 1, (2014), 62.

    Michael W. Botsko, An Elementary Proof of Lebesgue's Differentiation Theorem, Mathematical Advances in Translation, 32, No. 4 (2013), 379-382.

    *This article was translated and published in a Chinese journal of Mathematics. 

     

    Below are some articles and texts I enjoyed reading which are related to my work and have cited some of my papers.
     

    Solomon Leader, A Concept of Differential Based on Variational Equivalence under Generalized Riemann Integration, Real Analysis Exchange, 12, No. 1, (1986-87) 144-175. 

    D. Rutledge and R. Worth, A Comparison of two generalizations of the Riemann integral, Real Analysis Exchange, 13, No. 2, (1987-88) 432-435. 

    Charles Swartz and Brian S. Thomson, More on the Fundamental Theorem of Calculus, The American Mathematical Monthly, 95, No. 7 (1988) 644-648. 

    R. Vyborny  and R. Nester, First derivative tests for extrema, Int. J. Math. Educ. Sci. Technol., 1989, Vol. 20, No. 5 (1989) 755-762. 

    K. Klaimon, More applications of full covering, Pi Mu Epsilon Journal, 9, No. 3 (1990) 156-161. 

    T. Apostol; D. Mugler; D. Scott; A. Sterrett; A. Watkins “A Century of Calculus Part II :The Raymond W. Brink Selected Mathematical PapersThe Mathematical Association of America (1992).

    Charles Swartz, Even more on the Fundamental Theorem of Calculus, Proyecciones, 12, No. 2 (1993) 129-135. 

    Rudolf Výborný, Some applications of Kurzweil-Henstock integration, Mathematica Bohemica, Vol. 118 (1993), No. 4, 425–441. 

    D. J. Jeffrey, The Importance of Being Continuous, Mathematics Magazine, 67, No. 4 (1994) 294-300. 

    R. Vyborny, Existence of a Potential by Kurzweil-Henstock Integration, Proc. Centre Math. Appl. Austral. Nat. Univ. Nat. Univ., Canberra, 1994, 251-257. 

    Hubert Kalf, A Simple Proof that a bounded a.e. Continuous Function is Riemann Integrable, Classroom notes, (Received 22 August 1994) 628-631. 

    Tibor Salat, On full cover property of ordered fields, Mathematica Slovaca, Vol. 44 (1994), No. 5, 501-504.

    R. P. Boas, A Primer of Real Functions, 4th ed., Mathematical Association of America, Washington, D. C., 1996. 

    J. Klippert, Further Generalizations of the Fundamental Theorem of Calculus, Int. J. Math. Educ. Sci. Technol., 27, No. 3, (1996) 355-364.  

    Russell A. Gorden, The Use of Tagged Partitions in Elementary Real Analysis, The American Mathematical Monthly, 105, No. 2, (1998) 107-117. (my article cited in The Monthly, 105, No. 9 (1998) page 886)

     http://www.emis.de/proceedings/Toronto2000/papers/bullen.pdf 

    Charles Swartz, Introduction to Gauge Integrals, World Scientific, Singapore, 2001. 

    Robert G. Bartle, A Modern Theory of Integration, Graduate Studies in Mathematics, American Mathematical Society, 2001. 

    Hector J. Sussmann, Warga derivate containers and other generalized differentials, Proceedings of the 41st IEEE Conference on Decision and Control, December, 2002, 4728-4732.

    A. Aksoy and M. Martelli, The Wave Equation, Mixed Partial Derivatives, and Fubini's Theorem, The American Mathematical Monthly, 111, No. 4, (2004) 340-347. 

    J. Horvath, On the Riesz-Fischer Theorem, Studia Scientiarum Mathematicarum Hungarica, 41 (4) (2004) 467-478. 

    Roy M. Howard, Antiderivative series for differentiable functions, Int. J. Math. Educ. Sci. Technol , 35, No. 5, (2004) 725-731.

    J. J. Koliha, A Fundamental Theorem of Calculus for Lebesgue Integration, The American Mathematical Monthly, 113, No. 6, (2006) 551-554. 

    Roberto C. Cabrales & Marco A. Rojas-Medar, Sobre la diferenciabilidad de funciones en espacios de Banach, Revista Integracion, vol. 24, 2006, 87-100.

    Li, Yi Xia; Dong, Xin Han; Wang, Ti Fu, The Lebesgue measurability of the G integrable function, Acta Math. Appl. Sin., 30 (2007), No. 2, 327-333. 

    A Simplified multidimensional integral, Agnes M. Backhausz, Vilmos Komornik, and Tivadar Szilagyi, (2007)
    http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.0552v1.pdf  

    K. Hedayatian, A Generalized Integration by Parts, Int. J. Contemp. Math. Sciences, Vol. 2,2007, no. 28, 1367-1370.

    A change of variables theorem for the multidimensional Riemann integral
    Z Molnár, I Nagy, and T Szilágyi - Arxiv preprint arXiv:0804.2333, (2008) - arxiv.orghttp://arxiv.org/PS_cache/arxiv/pdf/0804/0804.2333v1.pdf  

    J J Koliha, Metrics, Norm and Integrals, World Scientific, Singapore, 2008. 

    Thomson, Bruckner, & Bruckner, Real Analysis, 2nd Edition, www.classicalrealanalysis.com 2008. 

    YAO Jing-sun, Some New Ways to Prove Rolle’s Theorem, College Mathematics, vol. 24, 2008, 131-133.

    J. J. Koliha, Mean, Meaner and the Meanest Mean Value Theorem, The American Mathematical Monthly, 116, No. 4, (2009) 356-361. 

    M. J. Evans and P. D. Humke, Revisiting a Century-Old Characterization of Baire Class One, Darboux Functions, The American Mathematical Monthly, 116, No. 5, (2009), 451-455.  

    J. Benedetto and W. Czaja, Integration and Modern Analysis, Birkhauser Advanced Texts, Boston, 2009. 

    K. Zangara and J. Marafino, Applications of full covers in real analysis,  Involve: A journal of mathematics, 2, No. 3 (2009) 297-304. 

    E. Godoy, El uso de cubiertas en la demostracion de teoremas del analisis real, Mosaicos Matematicos, No. 32, noviembre 2009, pp. 45-49. 

    ÁM Backhausz, V Komornik, T Szilágyi - A simplified multidimensional integral Czechoslovak Mathematical (2009) – Springer http://arxiv.org/pdf/0712.0552.pdf 

    S. R. Joshi and M. R. Gosavi, Mean Value Theorem, Bulletin of the Marathwada Math. Soc., Vol. 12, No. 1, June 2011, pp. 56-64.

    RL Pouso, A simple proof of the Fundamental Theorem of Calculus for the Lebesgue integral, http://arxiv.org/pdf/1203.1462.pdf 

    Patrick Landry Mombo Mingandza, Le Theoreme de Lebesgue sur la Derivabilite des Fonctions a Variation Bornee, Département de mathématiques et de statistique, Faculté des arts et des sciences, février 2012  https://papyrus.bib.umontreal.ca/jspui/bitstream/1866/6912/4/Mombo_Patrick_2012_memoire.pdf 

    Brian S. Thomson, THEORY OF THE INTEGRAL, ClassicalRealAnalysis.com (2012) http://classicalrealanalysis.info/documents/toti-June2012.pdf 

    Adimurthi, Shyam Sundar Ghoshal, and G. D. Veerappa Gowda, SBV regularity of an entropy solution for 1-d scalar conversation laws with non uniform convex flux (2012). https://lmb.univ-fcomte.fr/IMG/pdf/sbv.pdf

    Bernard Maurey and Jean-Pierre Tacchi, Sur le théorème de recouvrement de Vitali, Arch. Hist. Exact Sci. (2013) 67:81-118.

    "Measure, Integral, Derivative", by Sergei Ovchinnikov, Springer, 2013.

    Honors and Awards

    Student Government Award at Saint Vincent College – 1984

    C.A.S.E Nominee at Saint Vincent College – 1987

    Invited speaker at the Allegheny Mountain Section of the MAA – 1987
    – Full Covers and Riemann Integrability

    Teacher of the Year Award – The Allegheny Mountain Section of the MAA – 2003

    Boniface Wimmer Faculty Award at Saint Vincent College – 2003

    Invited speaker at the Allegheny Mountain Section of the MAA – 2004
    – On Derivatives

    Thoburn Award for Excellence in Teaching at Saint Vincent College - 2005

    Inclusion in the 2006 Edition of Who’s Who in America, 60th Diamond Edition, October 2005.