(in Japanese)

About me

I was a Global COE PD at Department of Mathematics at Kyoto University.

2000, Faculty of Science, Kyoto University
2004, Department of Mathematics at Kyoto University
2009/4-2013/3, GCOE-PD at Department of Mathematics at Kyoto University
2010/10-2012/3, Part-time teacher at Kyoto University(Additional)
2012/8- Part-time teacher at CJLC of Osaka University(Additional)
2013/4-, Part-time teacher at Kyoto Kyoiku University(Additional)


e-mail: y64k at chive.ocn.ne.jp (at should be replaced by @)

twitter: https://twitter.com/tyamada1093


My Interests

I am interested in easily stated problems in number theory and discrete mathematics. Many of such problems are formulated and discussed by elementary number theory, analytic number theory, combinatorics, graph theory, computability theory and others.

At present, my research interest lies in properties of values of classical arithmetic functions related to divisors of integers, such as σ and φ.


Course (2017)

Kyoto Kyoiku Univ. / Linear Algebra II (Apr.-Jul. / Fri / 12:50-14:20)

(7/25) Report Problems tex (in Japanese) pdf (in Japanese)

(6/17) Report Problems tex (in Japanese) pdf (in Japanese)

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Apr.-Jul. / Tue / 12:50-14:20)

(8/1) Extra exercises tex (in Japanese) pdf (in Japanese) (8/4 revised) tex (in Japanese) pdf (in Japanese) Figures (zip)


Course (2016)

Kyoto Kyoiku Univ. / Linear Algebra II (Apr.-Jul. / Fri / 12:50-14:20)

(7/28) Term-End Report Problems tex (in Japanese) pdf (in Japanese)

(6/17) Report Problems tex (in Japanese) pdf (in Japanese)


Course (2015)

Kyoto Kyoiku Univ. / Linear Algebra II (Apr.-Jul. / Fri / 12:50-14:20)

(7/28) Linear mappings between vector spaces tex (in Japanese) pdf (in Japanese)

(7/17) Term-End Report Problems tex (in Japanese) pdf (in Japanese)

(7/17) Sums and intersections of vector spaces tex (in Japanese) pdf (in Japanese)

(6/30) Vector spaces tex (in Japanese) pdf (in Japanese) (Addendum) tex (in Japanese) pdf (in Japanese)

(6/6) Report Problems tex (in Japanese) pdf (in Japanese)

(6/5) Linear transformations in plane and space tex (in Japanese) pdf (in Japanese)

(5/29) Vectors in plane and space tex (in Japanese) pdf (in Japanese)

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Apr.-Jul. / Tue / 12:50-14:20)

(8/20) Outline of answers of the examination problems tex (in Japanese) pdf (in Japanese)


Course (2014)

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Oct.-Feb. / Fri / 12:50-14:20)

(1/18) Calculation of fractions tex (in Japanese) pdf (in Japanese)

See old lecture notes for calculation of natural numbers.

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Apr.-Jul. / Tue / 12:50-14:20)

(7/29) The 5-6th lectures tex (in Japanese) pdf (in Japanese)

(7/29) The 4-5th lectures tex (in Japanese) pdf (in Japanese)

(7/22) The third-4th lectures tex (in Japanese) pdf (in Japanese)

(5/27) The second-third lectures tex (in Japanese) pdf (in Japanese)

(5/13) The first-second lectures tex (Unicode, in Japanese) pdf (in Japanese)

Course (2013)

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Apr.-Jul. / Tue / 12:50-14:20)

(5/7) The first lecture tex (Unicode, in Japanese) pdf (in Japanese)

(5/20) The second-third lecture tex (in Japanese) pdf


Course (2011)

Kyoto Univ. / Basic Mathematics IA (Fri / 8:45-10:15, 10:30-12:00)

The examination was held in July 29. It mainly concerns to convergence and limit of sequences and differentiation of functions.

Here is the homework given in Jul 8, Deadline Apr 5. It concerns to differentiation, integration and convergence of series. It is not obligatory.

Here is the homework given in May 20, Deadline July 1. It mainly concerns to convergence of real sequences. It is not obligatory.

Course (2010)

Kyoto Univ. / Linear Algebra B (Wed / 10:30-12:00)

The examination was held in January 26. It mainly concerns to linear mappings between vector spaces, the method of least squares and the eigenvalue problem.


A quiz was held in December 8. It mainly concerns to linear independence of vectors.


Documents

Proofs of the infinitude of primes (dvi)(1/12/2010, 8/7/2014 revised) (pdf) (8/7/2014 pdf updated TeX source(1/12/2010, 8/7/2014 revised)

Proofs of the fundamental theorem of arithmetic (dvi) (7/1/2015) Proofs of the fundamental theorem of arithmetic (pdf) (7/1/2015)TeX source (7/1/2015)


Publications

  1. Odd perfect numbers of a special form, Colloq. Math. 103 (2005), 303--307. dvi tex
  2. Unitary super perfect numbers, Math. Pannon. 19 (2008), 37--47. dvi tex
  3. Linear equations involving iterates of $\sigma(N)$, INTEGERS 9 supplement A15. dvi tex
  4. On diophantine equations $x^m=y^{n_1}+y^{n_2}+\ldots +y^{n_k}$, Glasgow Math. J. 51 (2009), 143--148. dvi tex
  5. On the simoultaneous equations $\sigma(2^a)=p^{f_1}q^{g_1}, \sigma(3^b)=p^{f_2}q^{g_2}, \sigma(5^c)=p^{f_3}q^{g_3}$, RIMS Kôkyûroku, (to appear). (Proceedings' paper of the workshop Analytic Number Theory -- Number Theory through Approximation and Asymptotics)
  6. Infinitary superperfect numbers Ann. Math. Inform. 47 (2017), 211--218, see the journal's website.


Talks

An exponential diophantine equation related to odd perfect numbers (at Diophantine Analysis and Related Fields 2018) pdf (3/4/2018) source (3/4/2018)


Links

arXiv.org

Number Theory Web

Number Theory List

The Mathematical Society of Japan

(2017/4/6 added)The On-Line Encyclopedia of Integer Sequences (OEIS)

inserted by FC2 system