Contact Information Email: pmusial@csu.edu Phone: (773) 995-2144

Education Ph D, University of Illinois at Chicago, 2002. Major: Mathematics Supporting Areas of Emphasis: Real Analysis Dissertation Title: The Lr Henstock Kurzweil Integral MS, University of Illinois at Chicago, 1997. Major: Mathematics Supporting Areas of Emphasis: Probability and Statistics BS, University of Illinois at Urbana-Champaign, 1984. Major: Mathematics

Professional Positions

• Assistant Professor, City Colleges of Chicago. (August 16, 1998 - August 15, 2002).
• Academic Advisor, Department, approximately 32 hours spent per year, 1. (January 1, 2018 - Present).
• Course Coordinator, Department, 2. (January 1, 2018 - May 15, 2021).
• PME Administrator, Department, 1.5. (January 1, 2017 - May 15, 2021).
• Math 0990 Level 1 coordinator, Department, 22.5. (August 15, 2005 - May 15, 2019).
• Committee Chair, University, 15. (August 16, 2010 - December 31, 2012).
• Academic Advisor, Department, 29. (August 16, 2005 - May 15, 2012).
• Academic Advisor, University, 13.5. (August 16, 2007 - December 31, 2008).
• Academic Advisor, College, 3. (August 16, 2006 - May 15, 2007).
• Academic Advisor, Department, 1. (August 16, 2005 - December 31, 2005).

Professional Memberships

• Mathematical Association of America. (June 25, 2010 - September 30, 2015).
• American Mathematical Society. (August 16, 2005 - January 1, 2015).

Publications

• Musial, P., Skvortsov, V. A., & Tulone, F. (2023). Comparison of the Pr-integral with Burkill’s integrals and some applications to trigonometric series. 523, 10 pages.
• Musial, P., Skvortsov, V., & Tulone, F. (2022). The HK_r-integral is not contained in the Pr-integral. 150(5), 2107–2144.
• Musial, P., Skvortsov, V., & Tulone, F. (2022). On Descriptive Characterizations of the HKr-Integral Recovering Function from its Lr-Derivative. Published.
• Musial, P., & Tulone, F. (2022). The Lr-Variational Integral. 2022, 10 pages.
• Musial, P., & Tulone, F. (2019). Dual of the Class of $HK_{r}$ Integrable Functions. 04 (2019)(1), 151–160.
• Musial, P., & Massarwi, E. (2015). A Stieltjes-Type Extension of the $L^{r}$ Perron Integral. 40(2), 291–308.
• Tulone, F., & Musial, P. (2015). Integration by parts for the $L^r$ Henstock-Kurzweil integral. 2015(44), 1–7.
• Sagher, Y., Siadat, M. V., & Musial, P. (2008). Keystone Method: A Learning Paradigm in Mathematics. 18(4), 337–348.
• Musial, P., & Sagher, Y. (2004). The $L^{r}$ Henstock-Kurzweil Integral. 160, 53–81.

Presentations

• Musial, P., 40th Summer Symposium in Real Analysis, "Dual of the Class of $HK_{r}$ Integrable Functions," Real Analysis Exchange, Sarajevo, Bosnia-Herzegovina. (June 21, 2016).
• Musial, P., 2016 Joint Mathematics Meetings, "Assessment of Student Learning in the Age of the Internet," Mathematical Association of America, Seattle. (January 6, 2016).
• Musial, P., AMS Central Fall Sectional Meeting, "Integrating the $L^{r}$ Derivative," American Mathematical Society, Loyola University, Chicago. (October 3, 2015).
• Musial, P., Conference In Analysis In Honor of Yoram Sagher, "Works Inspired by $HK_{r}$," Florida Atlantic University, Boca Raton, FL. (July 2, 2015).
• Musial, P., 39th Summer Symposium in Real Analysis, "Integration by Parts for the $L^{r}$ Henstock Kurzweil Integral," Real Analysis Exchange, Northfield, MN. (June 9, 2015).
• Musial, P. (Author & Presenter), 38th Summer Symposium in Real Analysis (City of a Hundred Spires Symposium), "A Stieltjes type extension of the Lr Perron integral (Joint work with E. Massarwi)," Czech Technical University, Prague, Czech Republic. (July 10, 2014).
• Musial, P. (Author & Presenter), 2014 Joint Mathematics Meetings, "Spice Up Your Real Analysis Class with In Class Presentations," American Mathematical Society and Mathematical Association of America, Baltimore, MD. (January 15, 2014).
• Musial, P. (Author & Presenter), 2013 Joint Mathematics Meetings, "Shortening the Path," American Mathematical Society and Mathematical Association of America, San Diego, CA. (January 12, 2013).
• Musial, P. (Author & Presenter), 2012 Joint Mathematics Meetings, "Using Illustrations to Motivate Definitions and Proofs in Real Analysis," American Mathematical Society and Mathematical Association of America, Baltimore, MD. (January 6, 2012).
• Musial, P. (Author & Presenter), 35th Summer Symposium in Real Analysis (Symposium on the Danube), "Functions of Lr-bounded variation," Renyi Mathematical Institute and Eotvos Lorand University, Budapest, Hungary. (June 5, 2011).
• Musial, P. (Author & Presenter), Conference of Workshops, "Game Theory 101," Metropolitan Mathematics Club of Chicago (MMC), Chicago, IL. (February 5, 2011).
• Musial, P. (Author & Presenter), 34th Summer Symposium in Real Analysis (Buckeye Symposium), "The Lr variational integral," College of Wooster, Wooster, OH. (July 16, 2010).
• Musial, P. (Author & Presenter), 33rd Summer Symposium in Real Analysis (Tall Grass Prairie Symposium), "New Results for the Lr Henstock Kurzweil Integral," Southeastern Oklahoma State University, Durant, OK. (June 25, 2009).
• Musial, P. (Author & Presenter), Annual Meeting, "Using Metaphor to Motivate Concepts in Real Analysis," Illinois Section of the Mathematical Association of America (ISMAA), Charleston, IL. (April 4, 2008).
• Musial, P. (Author & Presenter), Conference of Workshops, "Inspire Students with the TI N'Spire," Metropolitan Mathematics Club of Chicago (MMC), Chicago, IL. (January 26, 2008).
• Musial, P. (Author & Presenter), 2008 Joint Mathematics Meetings, "Using Metaphor to Motivate Concepts in Real Analysis," American Mathematical Society and Mathematical Association of America, San Diego, CA. (January 6, 2008).

Contract, Fellowships, Grants and Sponsored Research

• Musial, P., "Visit to University of Palermo," Sponsored by University of Palermo, Italy, Other, $1,300.00. (May 13, 2013 - May 28, 2013).
• Silver, H. (Co-Principal), Attele, K. R. (Co-Principal), Hrozencik, D. (Supporting), Musial, P. (Supporting), "Ensuring Mastery of Mathematics with Conceptual Tools and Gateways," Sponsored by CSU, Federal, $184,151.00. (October 1, 2006 - September 30, 2010).
• Humke, P. D. (Co-Principal), Musial, P. (Co-Principal), "32nd Summer Symposium in Real Analysis," Sponsored by Real Analysis Exchange, Federal, $15,000.00. (April 15, 2008 - March 31, 2009).

Research Activity

"Dual of the Class of $HK_{r}$ Integrable Functions" (On-Going). (January 30, 2017 - Present).
Abstract. We define for $1 ≤ r < ∞$ a norm for the class $HK_{r}$ of functions which are Henstock-Kurzweil integrable in Lr
sense. We then establish that the dual in this norm is isometrically isomorphic to $L_{r}$ and is therefore a Banach
space, and in the case $r = 2$, a Hilbert space.

"Extension of Henstock-Kurzweil integral" (Writing Results). (October 1, 2015 - Present).
We define an extension to the Henstock-Kurzweil integral.

"Functions of $L^{r}$ Bounded Variation" (On-Going). (January 1, 2015 - Present).
We define the $L^{r}$ variation of a function defined on a bounded interval and show that a function has finite $L^{r}$ variation if and only if it is BV in the classical sense on the interval.

"now" (On-Going). (May 1, 2014 - Present).
New work for Cello and Pure Data computer program

Teaching Experience

• MATH 1200, section 02, College Algebra. 3 credit hours. 22 enrolled.
• MATH 1195, section 02, College Algebra Lab. 2 credit hours. 16 enrolled.
• CPTR 5210, section 01, Graph Theory for Data Science. 3 credit hours. 19 enrolled.
• MATH 4410, section 01, Introduction to Real Variables. 3 credit hours. 3 enrolled.
• MATH 4650, section 01, Probability and Mathematical Statistics. 3 credit hours. 5 enrolled.
• MATH 1200, section 02, College Algebra. 3 credit hours. 27 enrolled.
• MATH 1195, section 02, College Algebra Lab. 2 credit hours. 17 enrolled.
• MATH 4250, section 61, Introduction to Modern Algebra I. 3 credit hours. 3 enrolled.
• MATH 5610, section 61, Mathematical Statistics. 3 credit hours. 9 enrolled.
• MATH 4940, section 61, Mathematics Seminar. 3 credit hours. 1 enrolled.
• MATH 1410, section 61, Calculus I. 4 credit hours. 24 enrolled.
• MATH 1200, section 01, College Algebra. 3 credit hours. 23 enrolled.
• MATH 1195, section 01, College Algebra Lab. 2 credit hours. 16 enrolled.
• CPTR 5210, section 01, Graph Theory for Data Science. 3 credit hours. 13 enrolled.
• MATH 4410, section 61, Introduction to Real Variables. 3 credit hours. 3 enrolled.
• MATH 4600, section 01, Introduction to Statistics. 4 credit hours. 3 enrolled.
• MATH 1210, section 01, College Alg & Trig. 3 credit hours. 17 enrolled.
• MATH 1200, section 04, College Algebra. 3 credit hours. 18 enrolled.
• MATH 1195, section 03, College Algebra Lab. 2 credit hours. 11 enrolled.
• MATH 4250, section 61, Intro Mod Algebra I. 3 credit hours. 7 enrolled.
• MATH 4940, section 01, Mathematics Seminar. 3 credit hours. 5 enrolled.
• MATH 1200, section 01, College Algebra. 3 credit hours. 25 enrolled.
• MATH 1195, section 01, College Algebra Lab. 2 credit hours. 20 enrolled.
• MATH 4410, section 61, Introduction to Real Analysis. 3 credit hours. 2 enrolled.
• MATH 4650, section 61, Probability and Mathematical Statistics. 3 credit hours. 7 enrolled.
• MATH 91277, section 5420-61, Analysis I. 3 credit hours. 3 enrolled.
• MATH 97341, section 1195-01, Coll Alg Lab. 2 credit hours. 17 enrolled.
• MATH 91223, section 1210-01, College Alg & Trig. 22 enrolled.
• MATH 91220, section 1200-02, College Algebra. 4 credit hours. 25 enrolled.
• MATH 91279, section 4250-61, Intro Mod Algebra I. 3 credit hours. 2 enrolled.
• MATH 94682, section 4940-01, Mathematics Seminar.
• MATH 2800, section 1, Discrete Math.MATH 4600, section 1, Intro Statistics.
• MATH 3800, section 61, Theory of Interest.
• MATH 5420, section 61, Analysis I. 3 credit hours. 4 enrolled.
• MATH 1400, section 61, Basic Calculus. 3 credit hours. 11 enrolled.
• MATH 1210, section 01, College Alg & Trig. 3 credit hours. 20 enrolled.
• MATH 1210, section 1, College Alg & Trig.
• MATH 3630, section 01, Review Actuary Exam. 2 credit hours. 2 enrolled.
• MATH 3630, section 1, Review Actuary Exam.
• MATH 1210, section 01, College Alg & Trig. 3 credit hours. 17 enrolled.
• MATH 2800, section 01, Discrete Math. 3 credit hours. 14 enrolled.
• MATH 5920, section 01, Graduate Seminar. 3 credit hours. 2 enrolled.
• MATH 3800, section 61, Theory of Interest. 3 credit hours. 4 enrolled.
• MATH 5420, section 61, Analysis I.
• MATH 1210, section 1, College Alg & Trig.
• MATH 1900, section 1, Intro Math Profssns.
• MATH 1020, section 61, Math for ELED Tch II.
• MATH 1210, section 1, College Alg & Trig.
• MATH 2800, section 1, Discrete Math.
• MATH 4600, section 1, Intro Statistics.
• MATH 1400, section 61, Basic Calculus.
• MATH 1210, section 1, College Alg & Trig.
• MATH 1900, section 1, Intro Math Profssns.
• MATH 3630, section 1, Review Actuary Exam.
• MATH 5470, section 61, Functional Analysis.
• MATH 4600, section 1, Intro Statistics.
• MATH 5610, section 61, Math Statistics I.
• MATH 1250, section 1, Pre-Calculus Math.
• MATH 3800, section 61, Theory of Interest.
• MATH 5420, section 61, Analysis I.
• MATH 1400, section 61, Basic Calculus.
• MATH 1210, section 1, College Alg & Trig.
• MATH 1900, section 1, Intro Math Profssns.
• MATH 3630, section 1, Review Actuary Exam.
• MATH 0990, section IB, Appl Intermed Algebra.
• MATH 990, section IB, Appl Intermed Algebra.
• MATH 1420, section 1, Calculus II.
• MATH 1250, section 1, Pre-Calculus Math.
• MATH 5420, section 61, Analysis I.
• MATH 1400, section 61, Basic Calculus.
• MATH 1210, section 1, College Alg & Trig.
• MATH 2300, section 1, Intro Higher Math.
• MATH 5430, section 61, Analysis II.
• MATH 2200, section 61, Linear Algebra.
• MATH 1250, section 1, Pre-Calculus Math.
• MATH 3800, section 1, Theory of Interest.
• MATH 5420, section 61, Analysis I.
• MATH 1400, section 1, Basic Calculus.
• MATH 2300, section 1, Intro Higher Math.
• MATH 3630, section 1, Review Actuary Exam.
• MATH 2430, section 1, Calculus III.
• MATH 5470, section 61, Functional Analysis.
• MATH 4410, section 1, Int Real Variables.
• HON 1355, section 1, Mathematical Inquiry.
• MATH 3800, section 61, Theory of Interest.
• MATH 5420, section 61, Analysis I.
• MATH 5610, section 61, Math Statistics I.
• MATH 5420, section 61, Analysis I.
• MATH 4600, section 61, Intro Statistics.
• MATH 3630, section 1, Review Actuary Exam.
• MATH 5430, section 61, Analysis II.
• MATH 4410, section 61, Int Real Variables.
• MATH 3800, section 1, Theory of Interest.
• MATH 5420, section 61, Analysis I.
• MATH 4600, section 1, Intro Statistics.
• MATH 3630, section 1, Review Actuary Exam.
• MATH 5610, section 61, Math Statistics I.
• MATH 5420, section 61, Analysis I.
• MATH 4600, section 1, Intro Statistics.
• MATH 4600, section 61, Intro Statistics.
• MATH 3630, section 1, Review Actuary Exam.
• MATH 3800, section 1, Theory of Interest.
• MATH 492, section 1, Graduate Seminar.
• MATH 461, section 61, Point Set Topology.
• MATH 313, section 1, Theory of Interest.
• MATH 5315, section 1, (Math 315/G) Intro Statistics.
• MATH 415, section 61, Analysis I.
• MATH 180, section 1, Intro Math Profssns.
• MATH 274, section 1, Review Actuary Exam.
• MATH 271, section 1, Differential Eqns.
• MATH 361, section 1, Intro Mod Algebra I.
• MATH 431, section 61, Par Diff Equations.
• MATH 274, section 1, Review Actuary Exam.
• MATH 313, section 1, Theory of Interest.
• MATH 5315, section 61, (315/G) Intro Statistics.
• MATH 415, section 61, Analysis I.
• MATH 180, section 1, Intro Math Profssns.
• MATH 140, section 1, Math for ELED Tch I.
• MATH 274, section 1, Review Actuary Exam.
• MATH 5361, section 1, (315/G) Intro Mod Algebra I.
• MATH 5345, section 61, (345/G) Hist of Mathematics.
• MATH 201, section 61, Linear Algebra.
• PHYS 345, section 1, Mathematical Methods.
• MATH 433, section 61, Adv Ordinary Diff.
• HON 130, section 1, Mathematical and Scientific Inquiry 1.
• MATH 392, section 61, Mathematics Seminar.

Directed Student Learning

• Master's Project Committee Chair, "Nonabsolute Integrals," MATH. (June 1, 2018 - December 1, 2018). Advised: Emmanuel Littrel
• Master's Project Committee Chair, "Nonparametric Statistics," MATH. (January 1, 2018 - May 1, 2018). Advised: Anita Hill
• Master's Project Committee Chair, "Analytic Continuation and the Riemann Zeta Function," MATH. (June 1, 2017 - May 1, 2018). Advised: LaNay Jackson
• Master's Thesis Committee Chair, "Multiple Approaches to the Hilbert Transform," MATH. (August 20, 2017 - December 15, 2017). Advised: Mouthana Shwayat
• Master's Project Committee Chair, "Game Theory: Nash Equilibria and Its Existence," MATH. (January 10, 2016 - May 15, 2016). Advised: Andre Gilford
• Master's Project Committee Chair, "Weak Convergence in Lp Spaces," MCSE. (August 16, 2013 - May 15, 2014). Advised: William Dennis
• Master's Thesis Committee Chair, "Riemann-Stieltjes integral and its extensions on Lr," MCSE. (June 1, 2013 - May 15, 2014). Advised: Eyad Massarwi
• Master's Project Committee Chair, "TBA," MCSE. (January 1, 2013 - May 17, 2013). Advised: JoVan Harrison
• Master's Project Committee Chair, "Mathematical Modelling in Beekeeping," MCSE. (January 1, 2011 - August 6, 2011). Advised: Alojz Jurcik
• Master's Project Committee Chair, "Path Derivatives and First-Return Analysis," MCSE. (February 28, 2008 - December 3, 2008). Advised: Piper Haywood
• Master's Project Committee Chair, "Fractal Geometry and Topological Dimension," MCSE. (February 1, 2008 - August 6, 2008). Advised: Brendan Coughlan
• Master's Thesis Committee Chair, "Investigation of the Henstock-Kurzweil Integral in n-Dimensional Space," MCSE. (January 15, 2008 - August 6, 2008). Advised: John Bialas
• Master's Thesis Committee Chair, "Demystifying Geometric Algebra," MCSE. (August 16, 2006 - August 5, 2007). Advised: Opal Jones

Faculty Development Activities Attended

Conference Attendance, "Faculty Resource Network Summer," New York University, New York, New York, USA. (June 11, 2018 - June 15, 2018).

University Service

• Faculty Advisor, Innovation Lab Symposia. (January 1, 2018 - Present).
• Committee Member, Search and Screen Committee Member. (January 1, 2018 - Present).
• Committee Member, PME (Planning, Measurement and Effectiveness) Steering Committee. (April 17, 2013 - Present).
• Invite Colloquium Speakers, Department Colloquia. (August 16, 2005 - Present).
• Faculty Mentor, Organize trip to Stickney Water Reclamation District plant. (June 26, 2018 - November 2, 2018).
• Committee Member, Illinois Articulation Initiative (IAI) General Education Mathematics Committee. (August 15, 2010 - August 15, 2018).
• Committee Officer, Faculty Senate. (August 16, 2017 - May 15, 2018).
• Committee Chair, Faculty Senate Buildings and Grounds Committee. (January 20, 2017 - May 15, 2018).
• Committee Member, Faculty Senate. (August 15, 2012 - May 15, 2018).
• Co-coordinator of high school math contest, Co-Coordinate ICTM Math contest. (January 1, 2008 - February 28, 2017).
• Committee Member, College of Pharmacy External DPC. (September 10, 2016 - October 5, 2016).
• Invite Yang Wang and assist with preparations, Invite Yang Wang as CSER Speaker. (October 31, 2014 - July 13, 2015).
• Committee Member, Police Chief Search. (April 2, 2015 - May 27, 2015).
• Committee Member, Search and Screen Committee. (August 16, 2013 - May 15, 2014).
• Committee Chair, Search and Screen Committee. (August 16, 2012 - May 15, 2013).
• Committee Member, Enrollment, Retention and Graduation Committee. (March 11, 2011 - November 12, 2012).
• Committee Member, Graduate Committee. (August 16, 2010 - May 15, 2011).
• Committee Member, University General Education Committee. (August 15, 2007 - May 15, 2010).
• Committee Member, HLC Focus Visit Task Force. (November 7, 2009 - April 12, 2010).
• Committee Member, 21st Century Academic Affairs Committee. (August 19, 2008 - August 19, 2009).
• Committee Member, Undergraduate Committee. (August 16, 2008 - December 31, 2008).
• Committee Member, CAS Secondary Education Committee. (January 1, 2008 - December 31, 2008).
• Committee Member, Admissions Counselor Search Committee. (February 1, 2008 - August 6, 2008).
• Committee Member, College of Education Dean Search Committee. (February 1, 2008 - August 6, 2008).
• Committee Chair, Undergraduate Committee. (August 16, 2005 - May 15, 2008).
• Committee Officer, CAS Curriculum Committee. (March 30, 2006 - March 27, 2008).
• Committee Member, Strategic Planning. (March 1, 2006 - April 30, 2007).

Professional Service

• Committee Member, Illinois Section of the Mathematical Association of America. (August 27, 2013 - August 15, 2016).
• Session Chair, Mathematical Association of America, Seattle, WA. (January 6, 2016 - January 9, 2016).
• Session Chair, American Mathematical Society, Chicago, IL. (October 3, 2015 - October 4, 2015).
• Committee Member, Conference in Analysis in Honor of Yoram Sagher, Boca Raton, FL. (February 9, 2015 - July 4, 2015).
• Conference-Related, Real Analysis Exchange, East Lansing, MI. (January 1, 2007 - December 31, 2008)

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