University of Calgary

Publications - 2010


Image of Advanced Number Theory with Applications

Advanced Number Theory with Applications

Mollin, Richard

This book is designed as a second course in number theory at the senior undergraduate/junior graduate level to follow a course in elementary methods, such as that given in my book Fundamental Number Theory with Applications, Second edition, published in 2008 and listed in this profile. Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and more than 1,500 entries in the index so that students can easily cross-reference and find the appropriate data. With numerous examples throughout, the text begins with coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density, and primes in arithmetic progression. It then applies these tools to Diophantine equations, before developing elliptic curves and modular forms. The text also presents an overview of Fermat’s Last Theorem (FLT) and numerous consequences of the ABC conjecture, including Thue–Siegel–Roth theorem, Hall’s conjecture, the Erdös–Mollin-–Walsh conjecture, and the Granville–Langevin Conjecture. In the appendix, the author reviews sieve methods, such as Eratothesenes’, Selberg’s, Linnik’s, and Bombieri’s sieves. He also discusses recent results on gaps between primes and the use of sieves in factoring. By focusing on salient techniques in number theory, this textbook provides the most up-to-date and comprehensive material for a second course in this field. It prepares students for future study at the graduate level.

 

A Dynamical Core for Topological Directed Graphs

Brenken, B.
 

A fourth-order finite difference method for solving the system of two-dimensional Burgers' equations

Liao, Wenyuan
 

A multiple model and Padé approximation, CREWES Research Report, Vol. 22, Chapter 93, p.1-11

Zhang, Dali, Lamoureux, Michael P. and Margrave, Gary F.
 

An efficient seventh power residue symbol algorithm

Caranay, Perlas and Scheidler, Renate
 

An explicit treatment of cubic function fields with applications

Landquist, Eric, Rozenhart, Pieter, Scheidler, Renate, Webster, Jonathan and Wu, Qingquan
 

A Note on Bartlett's M Test for Homogeneity of Variances

Zhang, L, Jiang, W and Chen, Gemai
 

A Note on Residuacity and Criteria for Prime Representation

Mollin, Richard and Srinivasan, Anitha
 

A note on the negative Pell equation

Mollin, Richard and Srinivasan, Anitha
 

Approximations for a Multivariate Hybrid Process with Applications to Change-Point Detection

Burke, Murray
 

A review of canonical forms for selfadjoint matrix polynomials.

Lancaster, Peter and Zaballa, I.
 

Bayesian Statistical Inference for Start-Up Demonstration Tests with Rejection of Units upon Observing d Failures

Scollnik, David
 

Central norms: Applications to Pell's equation

Mollin, Richard and Srinivasan, Anitha
 

Centred subpolytopes of the 4- cube

Bisztriczky, Ted, Boroczky, K., Fodor, F., Heppes, A. and Oliveros, D.
 

Classical Topics in Discrete Geometry

Bezdek, Karoly
 

Comparison of regression lines based on individual and averaged data

de Leon, Alexander, Wu, Beilei and Punzalan, JB
 

Construction of equally entangled bases in arbitrary dimensions via quadratic Gauss sums and graph states

Gheorghiu, Vlad and Shiang Yong Looi
 

Continuous Time Portfolio Selection under Conditional Capital at Risk

Dmitrasinovic-Vidovic, Gordana, Lari-Lavassani, Ali, Li, Xun and Ware, Antony
 

Covering large balls with convex sets in spherical space

Bezdek, Karoly and Schneider, Rolf
 

Cryptographic aspects of real hyperelliptic curves

Jacobson Jr., Michael J., Scheidler, Renate and Stein. Andreas
 

Current List of Publications

Scollnik, David
 

Distinguishing Number of Countable Homogeneous Relational Structures

Laflamme, Claude, Nguyen Van Thé, Lionel and Sauer, Norbert
 

Efficient reduction of large divisors on hyperelliptic curves

Avanzi, Roberto, Jacobson Jr., Michael J. and Scheidler, Renate
 

Ehrlich's theorem for groups

Li, Y. and Nicholson, W. Keith
 

Estimation of Q-factor and phase velocity using the recovered stress-strain relaxation spectrum, Proceedings of the GeoCanada 2010 meeting

Zhang, Dali, Lamoureux, Michael P and Margrave, Gary F
 

Evolution and Symmetry of Multipartite Entanglement

Gour, Gilad
 

Geochemical studies on the contamination and dispersion of heavy metals in intertidal sediments around a military air weapons shooting rage

Jung, HS, Yun, ST, Choi, BY, Kim, Hyang Mi, Jung, MC, Jung, MS and Kim, SO
 

Graph labelings and multipartite decompositions

Khan, Muhammad Ali
 

Hermitian quadratic matrix polynomials: solvents and inverse problems.

Lancaster, Peter and Tisseur, F.
 

Holomorphic semi-almost periodic functions

Brudnyi, Alex and Kinzebulatov, Damir
 

Local cloning of entangled states

Gheorghiu, Vlad, Li Yu and Scott M. Cohen
 

Location of quantum information in additive graph codes

Gheorghiu, Vlad, Shiang Yong Looi and Robert B. Griffiths
 

Minimum Hellinger distance estimation in a two-sample semiparametric model

Wu, Jingjing, Karunamuni, Rohana and Zhang, Biao
 

Mixed-outcome data

de Leon, Alexander and Carriere Chough, K in Encyclopedia of Biopharmaceutical Statistics (3rd ed)
 

Morphic groups

Li, Y., Nicholson, W. Keith and Zan, L.
 

On algebras of holomorphic functions with semi-almost periodic boundary values

Brudnyi, Alex and Kinzebulatov, Damir
 

On covering numbers of sublevel sets of analytic functions

Brudnyi, Alex
 

On Mean-Variance Portfolio Selection under a Hidden Markovian Regime Switching Model

Elliott, Robert, Siu, Tak Kuen and Badescu, Alexandru
 

On polynomial inequalities on exponential curves in C^n

Brudnyi, Alex, Bos, Len and Levenberg, Norm
 

On the optimal spectral abscissa for a system of linear oscillators.

Freitas, P. and Lancaster, Peter
 

Optimal component selection for component-based systems

Khan, Muhammad Ali and S. Mahmood in K. Elleithy Innovations in Computing Sciences and Software Engineering

In Component-based Software (CBS) development, it is desirable to choose software components that provide all necessary functionalities and at the same time optimize certain nonfunctional attributes of the system (for example, system cost). In this paper we investigate the problem of selecting software components to optimize one or more nonfunctional attributes of a CBS. We approach the problem through the lexicographic multi-objective optimization perspective and develop a scheme that produces Pareto-optimal solutions. Furthermore we show that the Component Selection Problem (CSP) can be solved in polynomial time if the components are connected by serial interfaces and all the objectives are to be minimized, whereas the corresponding maximization problem is NP-hard.

 

Pade approximations in inverse homogenization and numerical simulation of electromagnetic fields. URSI 2010 International Symposium on Electromagnetic Theory, IEEE Proceedings, Berlin, Germany, 978-1-4244-5154-8/10, 642-645

Cherkaev, Elena and Zhang, Dali
 

Parametrizing structure preserving transformations of matrix polynomials.

Lancaster, Peter and Zaballa, I.
 

Partition properties of the dense local order and a colored version of Milliken's theorem.

Laflamme, Claude, Nguyen Van Thé, Lionel and Sauer, Norbert
 

Projective free algebras of continuous functions on compact abelian groups

Brudnyi, Alex, Rodman, Leiba and Spitkovsky, Ilya M.
 

Proof of the Mollin-Srinivasan Conjecture and Other Class Number problems

Mollin, Richard and Srinivasan, Anitha
 

Quantitative bounds for Markov Chain Convergence: Wasserstein and Total Variation distances

Sezer, Deniz and Madras, Neal
 

Quantitative quality assessment of network-based schedules

Khan, Muhammad Ali and M. Siddiqui
 

Random generation of graphs with a given degree sequence

Khan, Muhammad Ali, K. K. Kayibi and S. Pirzada
 

Rational approximation for estimation of quality Q-factor and phase velocity in linear, viscoelastic, isotropic media

Zhang, Dali, Lamoureux, Michael P., Margrave, Gary F. and Cherkaev, Elena
 

Robust empirical Bayes tests for continuous distributions

Karunamuni, Rohana, Li, Jianjun and Wu, Jingjing
 

Schur decomposition of a matrix and the boundary of the pseudospectrum.

Boulton, L. and Lancaster, Peter
 

Security estimates for quadratic field based cryptosystems

Biasse, Jean-François, Jacobson, Jr., Michael J. and Silvester, Alan
 

Separable operations, graph codes and the location of quantum information

Gheorghiu, Vlad
 

Some algebraic aspects of the center problem for ordinary differential equations

Brudnyi, Alex
 

Stieltjes representation of the 3D Bruggeman effective medium and Pade approximation

Zhang, Dali, Cherkaev, Elena and Lamoureux, Miclael P.
 

Study behavior in a preparatory mathematics program: a case of bilingual Arab pre-University students

Khan, Muhammad Ali, M. Omar, M. Abujiya, B. Yushau and H. Al-Attas
 

The morphology of infinite tournaments; application to the growth of their profile.

Boudabbous, Youssef and Pouzet, Maurice
 

The ramification groups and different of a compositum of Artin-Schreier extensions

Wu, Qingquan and Scheidler, Renate
 

The T(5) property of families of overlapping unit disks

Bisztriczky, Ted, Boroczky, Karoly and Heppes, A.
 

Topological quivers as multiplicity free relations

Brenken, B.
 

Toward a Mackey formula for compact restriction of character sheaves

Cunningham, Clifton and Achar, Pramod
 

Translations in Affine Klingenberg Spaces

Bisztriczky, Ted and Lorimer, J. W.
 

Tree composition condition and moments vanishing

Brudnyi, Alex and Yomdin, Yosef
 

Visualizing minimal surfaces: rendering solid models with the aid of 3D printers, The Mathematica Journal:

Melko, Mike
 

Weighted Profile Least Squares Estimation for a Panel Data Varying-coefficient Partially Linear Model

Zhou, B, You, J, Xu, Q and Chen, Gemai
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