Faculty Profile

Pieter Allaart

Title
Professor
Department
Mathematics
College
College of Science

    

    

      


                          

            
Curriculum Vitae

            

              Click Here to View Faculty CV
            

          

        
                          

            
Education

            



  

  


  
PhD, Vrije Universiteit Amsterdam, 1998. 
Major: Mathematics & Computer Science
Dissertation Title: Ranges of vector measures and optimal-partitioning inequalities
MA, Free University, 1994. 
Major: Mathematics; Master's thesis: A constant-sum characterization of Benford's Law





          

        
                

          
Current Scheduled Teaching*


          
MATH 5120.001, Introduction to Analysis, Spring 2024 
MATH 3180.001, Probability for Engineers, Spring 2024 Syllabus
MATH 5900.723, Special Problems, Spring 2024 


          
*
  Texas Education Code 51.974 (HB 2504) requires each institution of
  higher education to make available to the public, a syllabus for
  undergraduate lecture courses offered for credit by the institution.
  

        

      

    

  


    

    

      


        


          


            
Previous Scheduled Teaching*


            
                    

                    MATH 5110.001, Introduction to Analysis, Fall 2023  SPOT
                    

                    MATH 4610.001, Probability, Fall 2023 Syllabus SPOT
                    

                    MATH 5900.719, Special Problems, Fall 2023 
                    

                    MATH 6950.712, Doctoral Dissertation, Spring 2023 
                    

                    MATH 5320.001, Real Analysis, Spring 2023  SPOT
                    

                    MATH 3680.004, Applied Statistics, Fall 2022 Syllabus SPOT
                    

                    MATH 3680.201, Applied Statistics, Fall 2022 Syllabus SPOT
                    

                    MATH 6950.708, Doctoral Dissertation, Fall 2022 
                    

                    MATH 4610.001, Probability, Fall 2022 Syllabus SPOT
                    

                    MATH 5310.001, Real Analysis, Fall 2022  SPOT
                    

                    MATH 5310.601, Real Analysis, Fall 2022  SPOT
                    

                    MATH 5900.716, Special Problems, Fall 2022 
                    

                    MATH 3510.001, Abstract Algebra I, Spring 2022 Syllabus SPOT
                    

                    MATH 6950.723, Doctoral Dissertation, Spring 2022 
                    

                    MATH 6810.001, Probability., Spring 2022  SPOT
                    

                    MATH 3510.001, Abstract Algebra I, Fall 2021 Syllabus SPOT
                    

                    MATH 6950.707, Doctoral Dissertation, Fall 2021 
                    

                    MATH 1780.003, Probability Models, Fall 2021 Syllabus SPOT
                    

                    MATH 3010.001, Seminar in Problem Solving Techniques, Fall 2021 
                    

                    MATH 6950.702, Doctoral Dissertation, Summer 5W1 2021 
                    

                    MATH 6950.702, Doctoral Dissertation, Spring 2021 
                    

                    MATH 4610.001, Probability, Spring 2021 Syllabus SPOT
                    

                    MATH 5320.001, Real Analysis, Spring 2021 Syllabus SPOT
                    

                    MATH 5320.601, Real Analysis, Spring 2021  SPOT
                    

                    MATH 5900.704, Special Problems, Spring 2021 
                    

                    MATH 6900.704, Special Problems, Spring 2021 
                    

                    MATH 6950.702, Doctoral Dissertation, Fall 2020 
                    

                    MATH 4610.001, Probability, Fall 2020 Syllabus SPOT
                    

                    MATH 5810.001, Probability and Statistics, Fall 2020  SPOT
                    

                    MATH 3010.001, Seminar in Problem Solving Techniques, Fall 2020 
                    

                    MATH 3510.001, Abstract Algebra I, Spring 2020 Syllabus
                    

                    MATH 6950.702, Doctoral Dissertation, Spring 2020 
                    

                    MATH 5320.001, Real Analysis, Spring 2020 
                    

                    MATH 6900.702, Special Problems, Spring 2020 
                    

                    MATH 6950.702, Doctoral Dissertation, Fall 2019 
                    

                    MATH 4610.001, Probability, Fall 2019 Syllabus SPOT
                    

                    MATH 5310.001, Real Analysis, Fall 2019  SPOT
                    

                    MATH 3010.001, Seminar in Problem Solving Techniques, Fall 2019 
                    

                    MATH 6950.702, Doctoral Dissertation, Spring 2019 
                    

                    MATH 2700.001, Linear Algebra and Vector Geometry, Spring 2019 Syllabus SPOT
                    

                    MATH 2700.002, Linear Algebra and Vector Geometry, Spring 2019 Syllabus SPOT
                    

                    MATH 6810.001, Probability., Spring 2019  SPOT
                    

                    MATH 6950.702, Doctoral Dissertation, Fall 2018 
                    

                    MATH 6950.705, Doctoral Dissertation, Fall 2018 
                    

                    MATH 3000.001, Real Analysis I, Fall 2018 Syllabus SPOT
                    

                    MATH 3010.001, Seminar in Problem Solving Techniques, Fall 2018 
                    

                    MATH 5900.702, Special Problems, Fall 2018 
                    

                    MATH 5900.726, Special Problems, Fall 2018 
                    

                    MATH 6950.702, Doctoral Dissertation, Spring 2018 
                    

                    MATH 3410.001, Differential Equations I, Fall 2017 Syllabus SPOT
                    

                    MATH 6950.702, Doctoral Dissertation, Fall 2017 
                    

                    MATH 6950.705, Doctoral Dissertation, Fall 2017 
                    

                    MATH 4610.001, Probability, Fall 2017 Syllabus SPOT
                    

                    MATH 3010.001, Seminar in Problem Solving Techniques, Fall 2017 
                    

                    MATH 3410.001, Differential Equations I, Spring 2017 Syllabus SPOT
                    

                    MATH 6950.702, Doctoral Dissertation, Spring 2017 
                    

                    MATH 3000.001, Real Analysis I, Spring 2017 Syllabus SPOT
                    

                    MATH 6900.702, Special Problems, Spring 2017 
                    

                    MATH 3410.007, Differential Equations I, Fall 2016 Syllabus SPOT
                    

                    MATH 6950.702, Doctoral Dissertation, Fall 2016 
                    

                    MATH 3000.001, Real Analysis I, Fall 2016 Syllabus SPOT
                    

                    MATH 3010.001, Seminar in Problem Solving Techniques, Fall 2016 
                    

                    MATH 6900.703, Special Problems, Fall 2016 
                    

                    MATH 6950.702, Doctoral Dissertation, Spring 2016 
                    

                    MATH 4610.001, Probability, Spring 2016 Syllabus SPOT
                    

                    MATH 6810.001, Probability., Spring 2016  SPOT
                    

                    MATH 6900.702, Special Problems, Spring 2016 
                    

                    MATH 6950.718, Doctoral Dissertation, Fall 2015 
                    

                    MATH 6950.721, Doctoral Dissertation, Fall 2015 
                    

                    MATH 5810.001, Probability and Statistics, Fall 2015  SPOT
                    

                    MATH 3000.001, Real Analysis I, Fall 2015 Syllabus SPOT
                    

                    MATH 3010.001, Seminar in Problem Solving Techniques, Fall 2015 
                    

                    MATH 5900.702, Special Problems, Fall 2015 
                    

                    MATH 6950.704, Doctoral Dissertation, Summer 5W1 2015 
                    

                    MATH 3410.003, Differential Equations I, Spring 2015 Syllabus
                    

                    MATH 3410.500, Differential Equations I, Spring 2015 Syllabus
                    

                    MATH 6950.702, Doctoral Dissertation, Spring 2015 
                    

                    MATH 5320.001, Functions of a Real Variable, Spring 2015 
                    

                    MATH 5900.702, Special Problems, Spring 2015 
                    

                    MATH 6900.702, Special Problems, Spring 2015 
                    

                    MATH 6950.721, Doctoral Dissertation, Fall 2014 
                    

                    MATH 5310.001, Functions of a Real Variable, Fall 2014 
                    

                    MATH 2730.003, Multivariable Calculus, Fall 2014 Syllabus
                    

                    MATH 2730.500, Multivariable Calculus, Fall 2014 Syllabus
                    

                    MATH 3010.001, Seminar in Problem Solving Techniques, Fall 2014 
                    

                    MATH 5900.715, Special Problems, Fall 2014 
                    

                    MATH 6900.770, Special Problems, Fall 2014 
                    

                    MATH 5900.701, Special Problems, Summer 10W 2014 
                    

                    MATH 3410.003, Differential Equations I, Spring 2014 Syllabus
                    

                    MATH 3410.500, Differential Equations I, Spring 2014 Syllabus
                    

                    MATH 6950.702, Doctoral Dissertation, Spring 2014 
                    

                    MATH 2700.003, Linear Algebra and Vector Geometry, Spring 2014 Syllabus
                    

                    MATH 5900.702, Special Problems, Spring 2014 
                    

                    MATH 6950.721, Doctoral Dissertation, Fall 2013 
                    

                    MATH 2730.003, Multivariable Calculus, Fall 2013 Syllabus
                    

                    MATH 2730.500, Multivariable Calculus, Fall 2013 
                    

                    MATH 5810.001, Probability and Statistics, Fall 2013 
                    

                    MATH 5900.715, Special Problems, Fall 2013 
                    

                    MATH 6900.770, Special Problems, Fall 2013 
                    

                    MATH 6950.716, Doctoral Dissertation, Spring 2013 
                    

                    MATH 2700.005, Linear Algebra and Vector Geometry, Spring 2013 Syllabus
                    

                    MATH 6810.001, Probability., Spring 2013 
                    

                    MATH 5900.707, Special Problems, Spring 2013 
                    

                    MATH 6950.721, Doctoral Dissertation, Fall 2012 
                    

                    MATH 2700.003, Linear Algebra and Vector Geometry, Fall 2012 Syllabus
                    

                    MATH 6810.001, Probability., Fall 2012 
                    

                    MATH 5900.715, Special Problems, Fall 2012 
                    

                    MATH 5320.001, Functions of a Real Variable, Spring 2012 
                    

                    MATH 2730.001, Multivariable Calculus, Spring 2012 
                    

                    MATH 5900.707, Special Problems, Spring 2012 
                    

                    MATH 5310.001, Functions of a Real Variable, Fall 2011 
                    

                    MATH 4610.001, Probability, Fall 2011 Syllabus
                    

                    MATH 5900.715, Special Problems, Fall 2011 
                    

                    MATH 4900.707, Special Problems, Summer 10W 2011 
                    

                    MATH 3680.002, Applied Statistics, Spring 2011 Syllabus
                    

                    MATH 2700.002, Linear Algebra and Vector Geometry, Spring 2011 Syllabus
                    

                    MATH 5900.707, Special Problems, Spring 2011 
                    

                    MATH 5900.708, Special Problems, Spring 2011 
                    

                    MATH 3680.002, Applied Statistics, Fall 2010 Syllabus
                    

                    MATH 2730.001, Multivariable Calculus, Fall 2010 Syllabus
                    

                    MATH 5900.715, Special Problems, Fall 2010 
                    

                    MATH 5900.765, Special Problems, Fall 2010 
                    

                    MATH 5320.001, Functions of a Real Variable, Spring 2010 
                    

                    MATH 2730.001, Multivariable Calculus, Spring 2010 
                    

                    MATH 5900.723, Special Problems, Spring 2010 
                    

                    MATH 4610.001, Probability, Fall 2008 
                    

                    MATH 5810.001, Probability and Statistics, Fall 2008 
                    

                    MATH 2510.001, Real Analysis I, Fall 2008 
                    

                    MATH 6900.770, Special Problems, Fall 2008 
                    

                    MATH 4900.001, Special Problems, Summer 3W1 2008 
                    

                    MATH 4900.705, Special Problems, Summer 5W2 2008 
                    

                    MATH 5900.001, Special Problems, Summer 10W 2008 
                    

                    MATH 2510.002, Real Analysis I, Spring 2008 
                    

                    MATH 5900.723, Special Problems, Spring 2008 
                    

                    MATH 5910.775, Special Problems, Spring 2008 
                    

                    MATH 6900.751, Special Problems, Spring 2008 
                    

                    MATH 1680.007, Elementary Probability and Statistics, Fall 2007 
                    

                    MATH 5350.002, Markov Processes, Fall 2007 
                    

                    MATH 4900.705, Special Problems, Summer 5W2 2007 
                    

                    MATH 1720.003, Calculus II, Spring 2007 
                    

                    MATH 5820.001, Probability and Statistics, Spring 2007 
                    

                    MATH 4650.001, Statistics, Spring 2007 
                    

                    MATH 1710.002, Calculus I, Fall 2006 
                    

                    MATH 2700.002, Linear Algebra and Vector Geometry, Fall 2006 
                    

                    MATH 2700.001, Linear Algebra and Vector Geometry, Summer 5W1 2006 
                    

                    MATH 5120.001, Introduction to Analysis, Spring 2006 
                    

                    MATH 2700.003, Linear Algebra and Vector Geometry, Spring 2006 
                    

                    MATH 5110.001, Introduction to Analysis, Fall 2005 
                    

                    MATH 1780.001, Probability Models, Fall 2005 
                    

                    MATH 1680.001, Elementary Probability and Statistics, Summer 5W2 2005 
                    

                    MATH 6940.700, Individual Research, Summer 8W1 2005 
                    

                    MATH 1720.020, Calculus II, Spring 2005 
                    

                    MATH 4650.001, Statistics, Spring 2005 
                    

                    MATH 1710.006, Calculus I, Fall 2004 
                    

                    MATH 4610.001, Probability, Fall 2004 
                    

                    MATH 5810.001, Probability and Statistics, Fall 2004 

          


          
*
  Texas Education Code 51.974 (HB 2504) requires each institution of
  higher education to make available to the public, a syllabus for
  undergraduate lecture courses offered for credit by the institution.
  

        

      

    

  

  
  	

	

	  

		

		   
Published Publications



  

  
Published Intellectual Contributions


  
Journal Article
Allaart, P. C., Kong, D.  (2023). Critical values for the beta-transformation with a hole at 0. Ergodic Theory and Dynamical Systems. 43(6), 1785-1828. 
Allaart, P. C., Jackson, S. C., Jones, R. T., Lambert, D.  (2023). On the existence of numbers with matching continued fraction and decimal expansions. Monatshefte für Mathematik. 202(1), 1-30. 
Allaart, P., Jones, R. T. (2023). Box-counting dimension and differentiability of box-like statistically self-affine functions. Journal of Mathematical Analysis and Applications. 521(2), Article 126909, 20 pages. 
Allaart, P. C., Kong, D.  (2022). Density spectrum of Cantor measure. Nonlinearity. 35(12), 6453–6484. 
Allaart, P. C., Kong, D.  (2021). Relative bifurcation sets and the local dimension of univoque bases. Ergodic Theory and Dynamical Systems. 41(8), 2241-2273. 
Allaart, P. C., Kong, D.  (2021). On the smallest base in which a number has a unique expansion. Transactions of the American Mathematical Society. 374(9), 6201-6249. 
Norouzi Kandalan, R., Allaart, P. C., Namuduri, K.  (2020). Mobility Accelerates Consensus-Building in Sensor Networks.. IEEE Sensors Letters. 4(12), 1-4. 
Allaart, P. C. (2020). The pointwise Holder spectrum of general self-affine functions on an interval.. Journal of Mathematical Analysis and Applications. 488(2), Article 124096, 35 pages. Elsevier. 
Allaart, P., Allen, A.  (2019). A random walk version of Robbins' problem: small horizon. Mathematica Applicanda. 47(2), 293-312. 
Allaart, P.  (2019). An algebraic approach to entropy plateaus in non-integer base expansions. Discrete and Continuous Dynamical Systems. 39(11), 6507-6522. 
Allaart, P., Kong, D.  (2019). On the continuity of the Hausdorff dimension of the univoque set. Advances in Mathematics. 354, 24 pages. 
Allaart, P., Kong, D., Baker, S.  (2019). Bifurcation sets arising from non-integer base expansions. Journal of Fractal Geometry. 6(4), 301-341. 
Allaart, P.  (2018). Differentiability and Holder spectra of a class of self-affine functions. Advances in Mathematics. 328, 1-39. 
Allaart, P.  (2017). Differentiability of a two-parameter family of self-affine functions. Journal of Mathematical Analysis and Applications. 450, 954-968. 
Allaart, P.  (2017). On univoque and strongly univoque sets. Advances in Mathematics. 308, 575-598. 
Allaart, P., Islas, J. A. (2016). A sharp lower bound for choosing the maximum of an independent sequence. Journal of Applied Probability. 53(4), 1041-1051. 
Allaart, P.  (2016). The infinite derivatives of Okamoto's function: an application of beta-expansions. Journal of Fractal Geometry. 3(1), 1-31. 
Allaart, P.  (2014). Correction and strengthening of ``How large are the level sets of the Takagi function?". 
Allaart, P.  (2014). Digital sum inequalities and approximate convexity of Takagi-type functions. 
Allaart, P.  (2014). Hausdorff dimension of level sets of generalized Takagi functions. 
Allaart, P.  (2014). On the level sets of the Takagi-van der Waerden functions. 
Allaart, P.  (2013). Level sets of signed Takagi functions. Acta Mathematica Hungarica. 
Allaart, P.  (2012). How large are the level sets of the Takagi function?. 
Allaart, P.  (2012). Predicting the supremum: optimality of "stop at once or not at all". 
Allaart, P.  (2012). The finite cardinalities of level sets of the Takagi function. 
Allaart, P.  (2012). The Takagi function: a survey. 
Allaart, P.  (2011). An inequality for sums of binary digits, with application to Takagi functions
 http://arxiv.org/abs/1009.1308


Related Links:
http://arxiv.org/abs/1009.1308. 
Kawamura, K., Allaart, P. C. (2011). Takagi function: Survey.  Denton:. 
Allaart, P.  (2010). A general `bang-bang' principle for predicting the maximum of a random walk.. 
Allaart, P.  (2010). How to stop near the top in a random walk. 
Allaart, P.  (2010). Optimal stopping rules for American and Russian options in a correlated random walk model.. 
Allaart, P.  (2010). The improper infinite derivatives of Takagi's nowhere-differentiable function. 
Allaart, P.  (2009). A sharp ratio inequality for optimal stopping when only relative record times are observed. 
Allaart, P.  (2009). Injectivity of the Dubins-Freedman construction of random  distributions. 
Allaart, P.  (2009). On a flexible class of continuous functions with uniform local structure. 
Allaart, P.  (2008). Distribution of the extrema of random Takagi functions. 
Allaart, P.  (2008). Optimal buy/sell strategies for directionally reinforced processes.. 
Allaart, P.  (2007). Dimensions of the coordinate functions of space-filling curves. 
Allaart, P.  (2007). Prophet inequalities for i.i.d. random variables with random arrival times. 
Allaart, P.  (2006). Extreme values of some continuous, nowhere differentiable functions. 
Allaart, P.  (2006). Prophet regions for discounted, uniformly bounded random variables. 
Allaart, P.  (2005). On the coordinate functions of L´evy's dragon curve. 
Allaart, P.  (2005). Prophet regions for independent [0, 1]-valued random variables with random dis-  counting. 
Allaart, P.  (2004). An application of prophet regions to optimal stopping with a random number of  observations. 
Allaart, P.  (2004). Optimal stopping rules for correlated random walks with a discount. 
Allaart, P.  (2004). Stopping the maximum of a correlated random walk, with cost for observation. 
Allaart, P.  (2003). Moments of the mean of Dubins-Freedman random probability distributions. 
Allaart, P.  (2003). Pseudo-prophet inequalities in average-optimal stopping. 
Allaart, P.  (2001). Optimal stopping rules for directionally reinforced processes. 
Allaart, P.  (2000). Inequalities relating maximal moments to other measures of dispersion. 
Allaart, P.  (1999). A sharp non-convexity bound for partition ranges of vector measures with atoms. 
Allaart, P.  (1999). Bounds on the non-convexity of ranges of vector measures with atoms. 
Allaart, P.  (1998). Minimax risk inequalities for the location-parameter classification problem. 
Allaart, P.  (1997). An invariant-sum characterization of Benford's law. Journal of Applied Probability. 34, 288-291. 



	
		
		
	  

	

	

  
    
	

	

	  

		

		   
Awarded Grants



  
  
  	  
          
Contracts, Grants and Sponsored Research  

 	 
	 	 
  
Grant - Research   
Allaart, P. C. (Principal), "Non-integer base expansions and multifractal analysis," Sponsored by Simons Foundation, Private, $42000 Funded. (September 2020 – August 2025).
Allaart, P. (Principal), "Visitor grant for a 2.5 month research visit to Utrecht University," Sponsored by NWO (Dutch National Science Foundation), International, $7000 Funded. (March 2018 – June 2018).



	
		
		
	  

	

	

	
	

  
  
  

  	

		

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					Overall
Summative Rating		
					Challenge and
Engagement Index		
					Response Rate
					
				

			
			
				

					
					
out of 5		
					
out of 7		
					%
 of 
students responded		
					
					
				

			
		


		
    
			
  • Overall Summative Rating (median):
    
			This rating represents the combined responses of students to the four global summative items and is presented to provide an overall index of the class’s quality. Overall summative statements include the following (response options include a Likert scale ranging from 5 = Excellent, 3 = Good, and 1= Very poor):
				
      
					
    • The course as a whole was
      • 
					
    • The course content was
      • 
					
    • The instructor’s contribution to the course was
      • 
					
    • The instructor’s effectiveness in teaching the subject matter was
      • 
				
    
			
    • 
			
  • Challenge and Engagement Index:
    
			This rating combines student responses to several SPOT items relating to how academically challenging students found the course to be and how engaged they were. Challenge and Engagement Index items include the following (response options include a Likert scale ranging from 7 = Much higher, 4 = Average, and 1 = Much lower):
				
      
					
    • Do you expect your grade in this course to be
      • 
					
    • The intellectual challenge presented was
      • 
					
    • The amount of effort you put into this course was
      • 
					
    • The amount of effort to succeed in this course was
      • 
					
    • Your involvement in course (doing assignments, attending classes, etc.) was
      • 
				
    
			
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