Timo Tossavainen

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All published works

Action	Title	Year	Authors
+	The congruence $x^n\equiv -a^n\pmod{m}$: Solvability and related OEIS sequences	2024	Jorma K. Merikoski Pentti Haukkanen Timo Tossavainen
+ PDF Chat	Programming as a mediator of mathematical thinking	2024	Timo Tossavainen Claes Johansson Alf Juhlin Anna Wedestig
+	We Can Differentiate Numbers, Too	2023	Timo Tossavainen Pentti Haukkanen Jorma K. Merikoski Mika Mattila
+	Exploring Perpendicularity and Parallelism Through Play	2023	Pentti Haukkanen Timo Tossavainen
+ PDF Chat	Cryptography based on algebraic perpendicularities	2023	Timo Tossavainen
+ PDF Chat	On the dimension of an Abelian group	2021	Timo Tossavainen Pentti Haukkanen
+	Complete Additivity, Complete Multiplicativity, and Leibniz-additivity on Rationals	2021	Jorma K. Merikoski Pentti Haukkanen Timo Tossavainen
+	An investigation of Swedish pre-service preschool teachers’ knowledge about the negative numbers	2020	Timo Tossavainen Maria Edholm Ewa-Charlotte Faarinen Maria Lundqvist
+	Asymptotics of partial sums of the Dirichlet series of the arithmetic derivative	2020	Pentti Haukkanen Jorma K. Merikoski Timo Tossavainen
+	Arithmetic Subderivatives : p-adic Discontinuity and Continuity	2020	Pentti Haukkanen Jorma K. Merikoski Timo Tossavainen
+ PDF Chat	Student teachers' definitions of the concept “teaching mathematics in preschool”	2019	Maria Johansson Timo Tossavainen Ewa-Charlotte Faarinen Anne Tossavainen
+	Arithmetic Subderivatives and Leibniz-Additive Functions	2019	Jorma K. Merikoski Pentti Haukkanen Timo Tossavainen
+ PDF Chat	Arithmetic subderivatives and Leibniz-additive functions	2019	Jorma K. Merikoski Pentti Haukkanen Timo Tossavainen
+	Arithmetic Subderivatives : Discontinuity and Continuity	2019	Pentti Haukkanen Jorma K. Merikoski Timo Tossavainen
+	Mathematics Studying Measure	2019	Timo Tossavainen Ewa-Charlotte Faarinen
+	Arithmetic Subderivatives and Leibniz-Additive Functions	2019	Jorma K. Merikoski Pentti Haukkanen Timo Tossavainen
+ PDF Chat	The arithmetic derivative and Leibniz-additive functions	2018	Pentti Haukkanen Jorma K. Merikoski Timo Tossavainen
+	THE SPECTRAL NORM OF A CIRCULANT MATRIX	2018	Jorma K. Merikoski Pentti Haukkanen Mika Mattila Timo Tossavainen
+ PDF Chat	SWEDISH PRIMARY AND PREPRIMARY STUDENT TEACHERS' VIEWS OF USING DIGITAL TOOLS IN PREPRIMARY MATHEMATICS EDUCATION	2018	Timo Tossavainen Maria Johansson Ewa-Charlotte Faarinen Anna Klisinska Anne Tossavainen
+	The arithmetic derivative and Leibniz-additive functions	2018	Pentti Haukkanen Jorma K. Merikoski Timo Tossavainen
+ PDF Chat	EXPLORATIONS OF FINNISH MATHEMATICS STUDENTS’ BELIEFS ABOUT THE NATURE OF MATHEMATICS	2018	Timo Tossavainen Antti Viholainen Mervi A. Asikainen Pekka E. Hirvonen
+ PDF Chat	On the spectral and Frobenius norm of a generalized Fibonacci r-circulant matrix	2018	Jorma K. Merikoski Pentti Haukkanen Mika Mattila Timo Tossavainen
+	The arithmetic derivative and Leibniz-additive functions	2018	Pentti Haukkanen Jorma K. Merikoski Timo Tossavainen
+ PDF Chat	Maximal perpendicularity in certain Abelian groups	2017	Mika Mattila Jorma K. Merikoski Pentti Haukkanen Timo Tossavainen
+	The spectral norm of a Horadam circulant matrix	2017	Jorma K. Merikoski Pentti Haukkanen Mika Mattila Timo Tossavainen
+	The Arithmetic Jacobian Matrix and Determinant	2017	Pentti Haukkanen Jorma K. Merikoski Mika Mattila Timo Tossavainen
+	The spectral norm of a Horadam circulant matrix	2017	Jorma K. Merikoski Pentti Haukkanen Mika Mattila Timo Tossavainen
+ PDF Chat	Varied ways to teach the definite integral concept	2013	Iiris Attorps Kjell Björk Mirko Radić Timo Tossavainen
+	Different aspects of the monotonicity of a function	2013	Timo Tossavainen Pentti Haukkanen Martti I. Pesonen
+ PDF Chat	Perpendicularity in an Abelian Group	2013	Pentti Haukkanen Mika Mattila Jorma K. Merikoski Timo Tossavainen
+	Can the Arithmetic Derivative be Defined on a Non-Unique Factorization Domain?	2013	Pentti Haukkanen Mika Mattila Jorma K. Merikoski Timo Tossavainen
+	A Mathematician Comes of Age by Steven G. Krantz	2012	Timo Tossavainen
+	Some South African mathematics Teachers' concept images of the equation concept	2012	Timo Tossavainen Iiris Attorps Pertti Väisänen
+	A generalization of Descartes’ rule of signs and fundamental theorem of algebra	2011	Pentti Haukkanen Timo Tossavainen
+	On mathematics students' understanding of the equation concept	2011	Timo Tossavainen Iiris Attorps Pertti Väisänen
+ PDF Chat	A distance estimate on the boundary of a conformal deformation of the unit ball satisfying a Harnack inequality and the Gehring-Hayman property	2010	Timo Tossavainen
+	Two Approaches to Geometrography	2010	Jorma K. Merikoski Timo Tossavainen
+	Conformal metrics on the unit ball: The Gehring-Hayman property and the volume growth	2009	Tomi Nieminen Timo Tossavainen
+	Means and the mean value theorem	2009	Jorma K. Merikoski Markku Halmetoja Timo Tossavainen
+	Fooling Newton's Method as Much as One Can	2009	Jorma K. Merikoski Timo Tossavainen
+	Fooling Newton's Method as Much as One Can	2009	Jorma K. Merikoski Timo Tossavainen
+	On the equivalence relation in the students' concept image of equation	2009	Iiris Attorps Timo Tossavainen
+	The Lost Cousin of the Fundamental Theorem of Algebra	2007	Timo Tossavainen
+	Boundary behavior of conformal deformations	2007	Tomi Nieminen Timo Tossavainen
+	On direct proportionality	2005	Markku Halmetoja Pentti Haukkanen Teuvo Laurinolli Jorma K. Merikoski Timo Tossavainen Ari Virtanen
+ PDF Chat	Conformal boundary and almost open balls	2004	Timo Tossavainen
+	PATHWISE CONNECTIVITY OF A CONFORMAL BOUNDARY	2003	Pekka Koskela Timo Tossavainen
+ PDF Chat	On nonnegative matrices with given row and column sums	2003	S. Drury Jorma K. Merikoski Virpi Laakso Timo Tossavainen

Common Coauthors

Coauthor	Papers Together
Jorma K. Merikoski	26
Pentti Haukkanen	25
Mika Mattila	9
Ewa-Charlotte Faarinen	4
Iiris Attorps	4
Pertti Väisänen	2
Markku Halmetoja	2
Tomi Nieminen	2
Maria Johansson	2
Anne Tossavainen	2
Virpi Laakso	1
Antti Viholainen	1
Anna Klisinska	1
Maria Edholm	1
Anna Wedestig	1
Alf Juhlin	1
Kjell Björk	1
S. Drury	1
Mirko Radić	1
Ari Virtanen	1
Maria Lundqvist	1
Pekka Koskela	1
Martti I. Pesonen	1
Pekka E. Hirvonen	1
Mervi A. Asikainen	1
Teuvo Laurinolli	1
Claes Johansson	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Remarks on an Arithmetic Derivative	1961	Ed Barbeau	7
+	The Arithmetic Derivative and Antiderivative	2012	Jurij Koviÿc	7
+ PDF Chat	Perpendicularity in an Abelian Group	2013	Pentti Haukkanen Mika Mattila Jorma K. Merikoski Timo Tossavainen	5
+	Conformal Metrics on the Unit Ball in Euclidean Space	1998	Mario Bonk Pekka Koskela Steffen Rohde	5
+	On mathematics students' understanding of the equation concept	2011	Timo Tossavainen Iiris Attorps Pertti Väisänen	4
+	How to differentiate a number	2003	Victor Ufnarovski Bo Åhlander	4
+ PDF Chat	Orthogonality relations on Abelian groups	1975	Gary Davis	3
+ PDF Chat	The arithmetic derivative and Leibniz-additive functions	2018	Pentti Haukkanen Jorma K. Merikoski Timo Tossavainen	3
+	Conformal metrics and size of the boundary	2002	Mario Bonk Pekka Koskela	3
+ PDF Chat	Boundary behavior of quasi-regular maps and the isodiametric profile	2001	Bruce Hanson Pekka Koskela Marc Troyanov	3
+ PDF Chat	Maximal perpendicularity in certain Abelian groups	2017	Mika Mattila Jorma K. Merikoski Pentti Haukkanen Timo Tossavainen	3
+	Handbook of Number Theory II	2004	József Sándor B. Crstici	2
+ PDF Chat	Rings with orthogonality relations	1971	Gary Davis	2
+	Does Understanding the Equal Sign Matter? Evidence from Solving Equations	2006	Eric Knuth Ana C. Stephens Nicole M. McNeil Martha W. Alibali	2
+ PDF Chat	Middle-School Students' Understanding of the Equal Sign: The Books They Read Can't Help	2006	Nicole M. McNeil Laura Grandau Eric Knuth Martha W. Alibali Ana C. Stephens Shanta Hattikudur Daniel E. Krill	2
+	Arithmetic Subderivatives : Discontinuity and Continuity	2019	Pentti Haukkanen Jorma K. Merikoski Timo Tossavainen	2
+	The Arithmetic Jacobian Matrix and Determinant	2017	Pentti Haukkanen Jorma K. Merikoski Mika Mattila Timo Tossavainen	2
+	Asymptotics of partial sums of the Dirichlet series of the arithmetic derivative	2020	Pentti Haukkanen Jorma K. Merikoski Timo Tossavainen	2
+ PDF Chat	On nonnegative matrices with given row and column sums	2003	S. Drury Jorma K. Merikoski Virpi Laakso Timo Tossavainen	2
+	On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin	1991	Anna Sfard	2
+	PATHWISE CONNECTIVITY OF A CONFORMAL BOUNDARY	2003	Pekka Koskela Timo Tossavainen	2
+	On the Dirichlet Convolution of Completely Additive Functions	2014	Isao Kiuchi Makoto Minamide	2
+	Arithmetic Subderivatives and Leibniz-Additive Functions	2019	Jorma K. Merikoski Pentti Haukkanen Timo Tossavainen	2
+ PDF Chat	Classical and new inequalities in analysis	1993	D. S. Mitrinović J. E. Pečarić A. M. Fink	1
+	New Designs for the Descartes Rule of Signs	2004	Michael Schmitt	1
+	Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers' Topic-Specific Knowledge of Students	2008	Heather C. Hill Deborah Loewenberg Ball S. Schilling	1
+	Different aspects of the monotonicity of a function	2013	Timo Tossavainen Pentti Haukkanen Martti I. Pesonen	1
+	A note on the fundamental theorem of algebra for the octonions	2007	Hugo Rodríguez-Ordóñez	1
+	Conformal metrics on the unit ball: The Gehring-Hayman property and the volume growth	2009	Tomi Nieminen Timo Tossavainen	1
+	Boundary behavior of conformal deformations	2007	Tomi Nieminen Timo Tossavainen	1
+ PDF Chat	On the Spectrum and Spectral Norms of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:math>-Circulant Matrices with Generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>-Horadam Numbers Entries	2014	Lele Liu	1
+	Lagrange's Proof of the Fundamental Theorem of Algebra	2006	Jeff Suzuki	1
+	Introduction to Calculus and Analysis	1989	Richard Courant Fritz John	1
+	The fundamental theorem of algebra	1998	Benjamin Fine Gerhard Rosenberger	1
+	Introduction to Arithmetical Functions	1985	Paul McCarthy	1
+	Aufbau der Geometrie aus dem Spiegelungsbegriff	1973	Friedrich Bachmann	1
+ PDF Chat	Classification and Concept Consistency	2011	Lara Alcock Adrian Simpson	1
+ PDF Chat	A probabilistic proof of the fundamental theorem of algebra	2004	Mihai N. Pascu	1
+	Mathematics learning in early childhood : paths toward excellence and equity	2009	Christopher T. Cross Taniesha A. Woods Heidi A. Schweingruber	1
+	Extension of quasiconformal mappings in three space	1965	F. W. Gehring	1
+	Another Short Proof of Descartes's Rule of Signs	2006	Vilmos Komornik	1
+	On multiple roots in Descartes’ Rule and their distance to roots of higher derivatives	2006	Arno Eigenwillig	1
+	Introduction to Abstract Algebra	1975	W. K. Nicholson	1
+	Descartes' Rule of Signs: Another Construction	1999	David J. Grabiner	1
+	Images of mathematics held by university teachers of mathematics education	1995	Roberta Mura	1
+	Definitions and examples in elementary calculus: the case of monotonicity of functions	2011	Cristina Bardelle Pier Luigi Ferrari	1
+	Some South African mathematics Teachers' concept images of the equation concept	2012	Timo Tossavainen Iiris Attorps Pertti Väisänen	1
+	Carlyle Circles and the Lemoine Simplicity of Polygon Constructions	1991	Duane W. DeTemple	1
+	Curvatures and Tolerances in the Euclidean Motion Group	2005	Hans-Peter Schröcker Johannes Wallner	1
+	On the london-hoffman inequality for the sum of elements of powers of nonnegative matrices	1991	Jorma K. Merikoski Ari Virtanen	1