Updated on 2024/12/25

写真a

 
HAYASAKA Futoshi
 
Organization
Faculty of Environmental, Life, Natural Science and Technology Professor
Position
Professor
Profile
可換環論の立場から、局所環上の加群に付随する諸概念（整閉包、重複度、Rees環など）の研究を行っています。 豊かで深い内容をもつイデアル論を加群論へと拡張し、先行するイデアルの場合の諸結果を統合するような理論の実現とその幾何学的意味の解明を目指しています。
External link

Degree

  • 博士（理学） ( 明治大学 )

Research Interests

  • local ring

  • graded ring

  • multiplicity

  • integral closure

  • module

  • Commutative Algebra

Research Areas

  • Natural Science / Algebra  / commutative ring theory

Education

  • Meiji University   理工学研究科   基礎理工学専攻

    2000.4 - 2005.3

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    Country： Japan

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Research History

  • 岡山大学環境生命自然科学学域 教授

    2023.4

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    Country：Japan

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  • 岡山大学環境生命科学学域 准教授

    2021.4 - 2023.3

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  • 岡山大学環境生命科学研究科 准教授

    2017.4 - 2021.3

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  • Hokkaido University of Education

    2013 - 2017

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  • Kagoshima National College of Technology

    2012 - 2013

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  • Kagoshima National College of Technology

    2010 - 2012

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Professional Memberships

 

Papers

  • Indecomposable integrally closed modules of rank 3 over two-dimensional regular local rings Reviewed International coauthorship International journal

    Futoshi Hayasaka, Vijay Kodiyalam

    Journal of Pure and Applied Algebra   228 ( 6 )   Paper No. 107612, 18 pp.   2024.1

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.jpaa.2024.107612

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  • Note on indecomposable integrally closed modules of rank 2 over two-dimensional regular local rings Reviewed International coauthorship International journal

    Futoshi Hayasaka, Vijay Kodiyalam

    Journal of Commutative Algebra   15 ( 4 )   513 - 518   2023.12

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Rocky Mountain Mathematics Consortium  

    DOI： 10.1216/jca.2023.15.513

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  • Indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring Reviewed International journal

    Futoshi Hayasaka

    Journal of Pure and Applied Algebra   226 ( 8 )   Paper No. 107026, 26 pp.   2022.8

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    Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.jpaa.2022.107026

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  • Constructing indecomposable integrally closed modules over a two-dimensional regular local ring Reviewed

    Futoshi Hayasaka

    Journal of Algebra   556   879 - 907   2020.8

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    Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.jalgebra.2020.03.029

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  • A formula for the associated Buchsbaum-Rim multiplicities of a direct sum of cyclic modules II Reviewed

    Futoshi Hayasaka

    Communications in Algebra   47 ( 8 )   3250 - 3263   2019

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  • A formula for the associated Buchsbaum–Rim multiplicities of a direct sum of cyclic modules Reviewed

    Futoshi Hayasaka

    Journal of Pure and Applied Algebra   222 ( 11 )   3774 - 3783   2018.11

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier B.V.  

    In this article, we compute the Buchsbaum–Rim function of two variables associated to a direct sum of cyclic modules and give a formula for the last positive associated Buchsbaum–Rim multiplicity in terms of the ordinary Hilbert–Samuel multiplicity of an ideal. This is a generalization of a formula for the last positive Buchsbaum–Rim multiplicity given by Kirby and Rees.

    DOI： 10.1016/j.jpaa.2018.02.006

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  • Asymptotic vanishing of homogeneous components of multigraded modules and its applications Reviewed

    Futoshi Hayasaka

    Journal of Algebra   513   1 - 26   2018

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  • A COMPUTATION OF BUCHSBAUM-RIM FUNCTIONS OF TWO VARIABLES IN A SPECIAL CASE Reviewed

    Futoshi Hayasaka

    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS   46 ( 5 )   1547 - 1557   2016

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ROCKY MT MATH CONSORTIUM  

    In this paper, we will compute Buchsbaum Rim functions of two variables associated to a parameter matrix of a special form over a one-dimensional Cohen Macaulay local ring, and we will determine when the function coincides with the Buchsbaum-Rim polynomial. As a consequence, we have that there exists the case where the function does not coincide with the polynomial function, which should be contrasted with the ordinary Buchsbaum Rim function of single variable.

    DOI： 10.1216/RMJ-2016-46-5-1547

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  • ASYMPTOTIC PERIODICITY OF PRIMES ASSOCIATED TO MULTIGRADED MODULES Reviewed

    Futoshi Hayasaka

    COMMUNICATIONS IN ALGEBRA   42 ( 6 )   2769 - 2778   2014.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：TAYLOR & FRANCIS INC  

    In this paper, we investigate the asymptotic behavior of the set of primes associated to a graded ring extension of Noetherian multigraded rings and modules, and prove that the periodicity occurs in a cone. We also prove the same asymptotic behavior of the grade. The previous known results on this subject are recovered as a special case.

    DOI： 10.1080/00927872.2013.774407

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  • ASYMPTOTIC PERIODICITY OF GRADE ASSOCIATED TO MULTIGRADED MODULES Reviewed

    Futoshi Hayasaka

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   140 ( 7 )   2279 - 2284   2012.7

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER MATHEMATICAL SOC  

    Let R be a Noetherian N-r-graded ring generated ill degrees d(1), ... , d(r) which are linearly independent vectors over R, and let a be an ideal in R-0. In this paper, we investigate the asymptotic behavior of the grade of the ideal a on the homogeneous components M-n of a finitely generated Z(r)-graclecl R-module M and show that the periodicity occurs in a cone.

    DOI： 10.1090/S0002-9939-2011-11370-4

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  • On the Buchsbaum-Rim function of a parameter module Reviewed

    Futoshi Hayasaka, Eero Hyry

    JOURNAL OF ALGEBRA   327 ( 1 )   307 - 315   2011.2

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    In this article, we prove that the Buchsbaum-Rim function l(A)(S(nu+1) (F)/N(nu+1)) of a parameter module N in F is bounded above by e(F/N)((nu+d+r-1)(d+r-1)) for every integer nu >= 0. Moreover, it turns out that the base ring A is Cohen-Macaulay once the equality holds for some integer nu. As a direct consequence, we observe that the first Buchsbaum-Rim coefficient e(1)(F/N) of a parameter module N is always non-positive. (C) 2010 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.jalgebra.2010.09.035

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  • A NOTE ON THE BUCHSBAUM-RIM MULTIPLICITY OF A PARAMETER MODULE Reviewed

    Futoshi Hayasaka, Eero Hyry

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   138 ( 2 )   545 - 551   2010.2

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER MATHEMATICAL SOC  

    In this article we prove that the Buchsbaum-Rim multiplicity e(FIN) of a parameter module N in a free module F = A(r) is bounded above by the colength l(A)(F/N). Moreover, we prove that once the equality l(A)(F/N) = e(F/N) holds true for some parameter module N in F, then the base ring A is Cohen-Macaulay.

    DOI： 10.1090/S0002-9939-09-10119-3

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  • On vanishing of certain Ext modules Reviewed

    Shiro Goto, Futoshi Hayasaka, Ryo Takahashi

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   60 ( 4 )   1045 - 1064   2008.10

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：MATH SOC JAPAN  

    Let R be a Noetherian local ring with the maximal ideal m and dim R = 1. In this paper, we shall prove that the module ExtR(R)(1)(R/Q,R) does not vanish for every parameter ideal Q in R, if the embedding dimension v(R) of R is at most 4 and the ideal m(2) kills the 0th local cohomology module H-m(0)(R). The assertion is no longer true unless v(R) <= 4. Counterexamples are given. We shall also discuss the relation between our counterexamples and a problem on modules of finite G-dimension.

    DOI： 10.2969/jmsj/06041045

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  • A Family of Graded Modules Associated to a Module Reviewed

    Futoshi Hayasaka, Eero Hyry

    COMMUNICATIONS IN ALGEBRA   36 ( 11 )   4201 - 4217   2008

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：TAYLOR & FRANCIS INC  

    In this article we introduce a certain family of graded modules associated to a given module. These modules provide a natural extension of the notion of the associated graded ring of an ideal. We will investigate their properties. In particular, we will try to extend Ree' theorem on the associated graded ring of an ideal generated by a regular sequence to this context.

    DOI： 10.1080/00927870802177291

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  • Asymptotic stability of primes associated to homogeneous components of multigraded modules Reviewed

    Futoshi Hayasaka

    JOURNAL OF ALGEBRA   306 ( 2 )   535 - 543   2006.12

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Let A subset of B be a homogeneous extension of Noetherian standard N-r-graded rings with A(0) = B-0 = R. Let M be a finitely generated N-r-graded B-module and N subset of M a finitely generated graded A-submodule of M. In this paper, we investigate the asymptotic behavior of the set of primes associated to the module M-n/N-n and prove that for all sufficiently large n epsilon N-r, the set Ass(R)(M-n/N-n) is stable. We also give a certain inequality for the spread of standard multigraded rings, which is a natural generalization of Burch's inequality for the analytic spread of an ideal. (c) 2006 Published by Elsevier Inc.

    DOI： 10.1016/j.jalgebra.2006.03.020

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  • Rees algebras of the second syzygy module of the residue field of a regular local ring Reviewed

    S. Goto, F. Hayasaka, K. Kurano, Y. Nakamura

    Contemporary Mathematics   390   97 - 108   2005

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    Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：AMER MATHEMATICAL SOC  

    Let (A, m) be a regular local ring and let M subset of F = A(d) be the second syzygy module of the residue field A/m. In this paper, we introduce the concept of generalized Grassmann algebras and investigate the Rees algebra R(M) of M. We explore the properties of generalized Grassmann algebras and prove that the Rees algebra R(M) of the second syzygy module M is a Gorenstein factorial domain.

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  • The a-invariant and Gorensteinness of graded rings associated to filtrations of ideals in regular local rings Reviewed

    Shiro Goto, Futoshi Hayasaka, Shin-Ichiro Iai

    Proceedings of the American Mathematical Society   131 ( 1 )   87 - 94   2003.1

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    Language：English   Publishing type：Research paper (scientific journal)  

    Let A be a regular local ring and let ℱ = {Fn}n∈Zdbl
    be a filtration of ideals in A such that ℛ(ℱ) = ⊕n≥0 Fn is a Noetherian ring with dim ℛ(ℱ) dim A + 1. Let script G sign (ℱ) = ⊕n≥0 Fn/Fn+1 and let a(script G sign(ℱ)) be the a-invariant of script G sign(ℱ). Then the theorem says that F1 is a principal ideal and Fn = F1n for all n ∈ Zdbl
    if and only if script G sign (ℱ) is a Gorenstein ring and a script G sign(ℱ)) = -1. Hence a script G sign(ℱ)) ≤ -2, if script G sign (ℱ) is a Gorenstein ring, but the ideal F1 is not principal.

    DOI： 10.1090/S0002-9939-02-06635-2

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  • Towards a theory of Gorenstein m-primary integrally closed ideals Reviewed

    S. Goto, F. Hayasaka, S. Kasuga

    COMMUTATIVE ALGEBRA, SINGULARITIES AND COMPUTER ALGEBRA   115   159 - 177   2003

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    Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER  

    Let A be a Noetherian local ring with the maximal ideal m and d = dim A. The set X-A of Gorenstein m-primary integrally closed ideals in A is explored in this paper. If k = A/m is algebraically closed and d greater than or equal to 2, then X-A is infinite. In contrast, for each field k which is not algebraically closed and for each integer d greater than or equal to 0, there exists a Noetherian complete equi-characteristic local integral domain A with dim A = d such that (1) the normalization of A is regular, (2) X-A = {m}, and (3) k = A/m. When d = 1, X-A is finite if and only if (A) over cap /p is not a DVR for any p is an element of Min (A) over cap, where (A) over cap denotes the m-adic completion. The list of elements in X-A is given, when A is a one-dimensional Noetherian complete local integral domain.

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  • Finite homological dimension and primes associated to integrally closed ideals Reviewed

    S. Goto, F. Hayasaka

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   130 ( 11 )   3159 - 3164   2002

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER MATHEMATICAL SOC  

    Let I be an integrally closed ideal in a commutative Noetherian ring A. Then the local ring A(p) is regular (resp. Gorenstein) for every p epsilon Ass(A)A/I if the projective dimension of I is finite (resp. the Gorenstein dimension of I is finite and A satisfies Serre's condition (S-1)).

    DOI： 10.1090/S0002-9939-02-06436-5

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  • Finite homological dimension and primes associated to integrally closed ideals II Reviewed

    Shiro Goto, Futoshi Hayasaka

    J. Math. Kyoto Univ.   42 ( 4 )   631 - 639   2002

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MISC

  • Modules of reduction number one

    Futoshi Hayasaka

    Preprint (math.AC/0612741)   2006

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    Language：English   Publishing type：Internal/External technical report, pre-print, etc.  

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Presentations

  • On ideals of indecomposable integrally closed modules over two-dimensional regular local rings

    Futoshi Hayasaka

    2022.11.18 

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    Event date： 2022.11.14 - 2022.11.18

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  • A note on the Buchsbaum-Rim multiplicity of modules over a two-dimensional regular local ring

    早坂太

    第42回可換環論シンポジウム  2021.11.21 

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    Event date： 2021.11.20 - 2021.11.22

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  • 単項式イデアルに付随する高階数直既約整閉加群 Invited

    早坂太

    可換環論オンラインワークショップ  2020.11.23 

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    Event date： 2020.11.21 - 2020.11.23

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  • ２次元正則局所環上の直既約整閉加群について Invited

    早坂太

    特異点セミナー  2022.7.25 

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  • ２次元正則局所環上の階数２の直既約整閉加群

    早坂太

    第33回可換環論セミナー  2022.6.16 

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  • 正則局所環上の加群の整閉包 Invited

    早坂 太

    日本数学会秋季分科会  2019.9.18 

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    Language：Japanese   Presentation type：Oral presentation (invited, special)  

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  • Indecomposable integrally closed modules associated to complete monomial ideals Invited International conference

    早坂 太

    Special Session on Commutative Algebra and its Environs, 1147th AMS MEETING  2019.3.23 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  • 整閉単項式イデアルに付随する直既約整閉加群について Invited

    東大可換環論セミナー  2018.12.10 

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    Language：Japanese  

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  • Construction of indecomposable integrally closed modules over a two-dimensional regular local ring

    HAYASAKA Futoshi

    The 40th symposium on commutative algebra in Japan  2018.11.25 

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    Language：English   Presentation type：Oral presentation (general)  

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  • On constructiong integrally closed modules over a two-dimensional regular local ring Invited International conference

    Futoshi Hayasaka

    The 10th Japan-Vietnam Joint Seminar on Commutative Algebra  2018.9.14 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  • 2次元正則局所環の整閉イデアルに付随する整閉加群の構成

    第20回岡山可換代数表現セミナー  2018.6.11 

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    Language：Japanese  

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  • A note on constructing integrally closed modules over a two-dimensional regular local ring

    Mini-workshop on Commutative Algebra  2018.3.27 

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  • 多重次数付き加群の節減と単項式イデアルの整閉性

    日本数学会  2018.3.20 

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  • On the associated Buchsbaum-Rim multiplicities of a direct sum of cyclic modules

    第39回可換環論シンポジウム  2017.11.17 

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  • Existence of complete reductions and normality of monomial ideals

    第16回岡山可換代数表現セミナー  2017.4.20 

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  • On existence of complete and joint reductions of multigraded modules Invited International conference

    International Workshop on Commutative Algebra  2017.1.7 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  • Vanishing of homogeneous components and spread of multigraded modules

    第38回可換環論シンポジウム  2016.11.19 

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  • 巡回加群の直和の随伴ブックスバウム・リム重複度公式

    日本数学会  2016.9.16 

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  • Serre's conditions (S2) and (R1) Invited International conference

    The 2nd international school on commutative algebra at Thai Nguyen University  2016.6.9 

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    Language：English   Presentation type：Oral presentation (general)  

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  • The associated graded rings of ideals generated by regular sequences Invited International conference

    The 2nd international school on commutative algebra at Thai Nguyen University  2016.6.7 

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    Language：English   Presentation type：Oral presentation (general)  

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  • A formula for the associated Buchsbaum-Rim multiplicity of a direct sum of cyclic modules Invited International conference

    International conference and the 8th Japan-Vietnam Joint Seminar on Commutative Algebra  2016.3.25 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  • Computations of the associated Buchsbaum-Rim multiplicities of a direct sum of cyclic modules

    第37回可換環論シンポジウム  2015.11.20 

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  • Buchsbaum-Rim multiplicities of a direct sum of cyclic modules Invited

    第60回代数学シンポジウム  2015.8.31 

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    Language：Japanese   Presentation type：Oral presentation (invited, special)  

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  • 加群の重複度と整閉包 Invited

    早坂 太

    明治大学大学院集中講義  2013.9 

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  • Buchsbaum-Rim multiplicity and its generalization Invited

    南九州代数系集会  2013.8 

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  • Asymptotic behavior of primes associated to multigraded modules Invited International conference

    The 7th Japan-Vitenam Joint Seminar on Commutative Algebra  2011.12 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  • 加群のブックスバウム・リム関数 Invited

    第141回数理情報科学談話会（鹿児島大学）  2010.7 

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    Language：Japanese  

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  • The Buchsbaum-Rim function of a parameter module Invited International conference

    The 5th Japan-Vietnam Joint Seminar on Commutative Algebra  2010.1 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  • The Buchsbaum-Rim function of a parameter module

    早坂 太

    第42回環論および表現論シンポジウム  2009.10 

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  • The Buchsbaum-Rim function of a parameter module Invited

    早坂 太

    Summer seminar on ring theory  2009.6 

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  • On the Buchsbaum-Rim multiplicity of a parameter module Invited International conference

    The 4th Japan-Vietnam Joint Seminar on Commutative Algebra  2009.2 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  • A family of graded modules associated to a module Invited International conference

    International Conference in Commutative Algebra  2008.1 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  • On certain graded modules associated to a module Invited International conference

    早坂 太

    The 3rd Japan-Vietnam Joint Seminar on Commutative Algebra  2007.12 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  • On modules of reduction number one International conference

    The 2nd Japan-Vietnam Joint Seminar on Commutative Algebra  2006.3 

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    Language：English  

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  • Modules of reduction number one International conference

    Nebraska Commutative Algebra Conference: WiegandFest  2005.5 

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    Language：English  

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  • 加群のRees環入門

    早坂 太

    第1回可換環論サマースクール  2004.1 

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  • Rees algebras of modules over a regular local ring Invited International conference

    Session for Young Researchers in Commutative Algebra and Algebraic Geometry  2003.12 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  • Rees algebras of the second syzygy modules Invited International conference

    Commutative Algebra and its Interaction with Algebraic Geometry  2003.6 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  • Finite homological dimension and primes associated to integrally closed ideals International conference

    Conference on Commutative Algebra 2001  2001.8 

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    Language：English   Presentation type：Oral presentation (general)  

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Research Projects

  • 整閉包の理論の新展開と局所環論への応用

    Grant number：20K03535  2020.04 - 2023.03

    日本学術振興会  科学研究費助成事業  基盤研究(C)

    早坂 太

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    Grant amount：\3380000 （ Direct expense: \2600000 、 Indirect expense：\780000 ）

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  • 次数付き環拡大に付随する関数と重複度の研究

    2012.04 - 2015.03

    科学技術研究費補助金  若手研究(B) 

    早坂 太

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    Authorship：Principal investigator  Grant type：Competitive

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  • 局所環上の巴系加群の重複度の基礎理論構築

    2010.04 - 2012.03

    科学技術研究費補助金  若手研究(B) 

    早坂 太

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    Authorship：Principal investigator  Grant type：Competitive

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Class subject in charge

  • Internship （2024academic year） Summer concentration  - その他

  • Internship （2024academic year） Summer concentration  - その他

  • Foundation of Algebra 1 （2024academic year） 1st semester  - 月1,木3

  • Foundation of Algebra 2 （2024academic year） 1st semester  - 月2,木4

  • Keys in Algebra 1 （2024academic year） Third semester  - 火5,金5

  • Keys in Algebra 2 （2024academic year） Third semester  - 火6,金6

  • Foundations of Algebra （2024academic year） 1st semester  - 月1～2,木3～4

  • Applications of Algebra （2024academic year） Third semester  - 火5～6,金5～6

  • Technical English （2024academic year） 3rd and 4th semester  - [第３学期]水3～4, [第４学期]水1～2

  • Foundations of Geometry （2024academic year） Summer concentration  - その他5～6

  • Foundation of Geometry A （2024academic year） Summer concentration  - その他

  • Foundation of Geometry B （2024academic year） Summer concentration  - その他

  • Topics in Applied Commutative Algebra （2024academic year） Late  - その他

  • Seminar in Applied Mathematics A （2024academic year） Year-round  - その他

  • Seminar in Applied Mathematics A （2024academic year） Year-round  - その他

  • Seminar in Applied Mathematics B （2024academic year） Year-round  - その他

  • Seminar in Applied Mathematics B （2024academic year） Year-round  - その他

  • Advanced Seminar in Applied Mathematics （2024academic year） Year-round  - その他

  • Applied Computational Algebra （2024academic year） Late  - 金7～8

  • Advanced Mathematical Science in Liberal Arts （2024academic year） Third semester  - 水3～4

  • Advanced Study （2024academic year） Other  - その他

  • Linear Algebra III-1 （2024academic year） special  - その他

  • Linear Algebra 1 （2024academic year） Third semester  - 月7～8

  • Linear Algebra 2 （2024academic year） Fourth semester  - 月7～8

  • Introduction to Discrete Mathematics （2024academic year） Fourth semester  - 月1～2,木5～6

  • Introduction to Discrete Mathematics 1 （2024academic year） Fourth semester  - 月1,木5

  • Introduction to Discrete Mathematics 2 （2024academic year） Fourth semester  - 月2,木6

  • Foundation of Algebra 1 （2023academic year） 1st semester  - 月1,木3

  • Foundation of Algebra 2 （2023academic year） 1st semester  - 月2,木4

  • Keys in Algebra 1 （2023academic year） Third semester  - 火5,金5

  • Keys in Algebra 2 （2023academic year） Third semester  - 火6,金6

  • Foundations of Algebra （2023academic year） 1st semester  - 月1～2,木3～4

  • Applications of Algebra （2023academic year） Third semester  - 火5～6,金5～6

  • Introduction to Commutative Algebra （2023academic year） Late  - 木3～4

  • Topics in Commutative Algebra （2023academic year） Prophase  - その他

  • Technical English （2023academic year） 3rd and 4th semester  - [第３学期]水3～4, [第４学期]水1～2

  • Foundations of Geometry （2023academic year） 1st and 2nd semester  - 水5～6

  • Foundation of Geometry A （2023academic year） 1st semester  - 水5～6

  • Foundation of Geometry B （2023academic year） Second semester  - 水5～6

  • Topics in Applied Algebra （2023academic year） Late  - 木3～4

  • Topics in Applied Commutative Algebra （2023academic year） Late  - その他

  • Seminar on Applied Mathematics （2023academic year） Prophase  - その他

  • Seminar in Applied Mathematics （2023academic year） Late  - その他

  • Seminar on Applied Mathematics （2023academic year） Late  - その他

  • Seminar in Applied Mathematics （2023academic year） Prophase  - その他

  • Seminar in Applied Mathematics A （2023academic year） Year-round  - その他

  • Seminar in Applied Mathematics A （2023academic year） Year-round  - その他

  • Seminar in Applied Mathematics B （2023academic year） Year-round  - その他

  • Seminar in Applied Mathematics B （2023academic year） Year-round  - その他

  • Advanced Seminar in Applied Mathematics （2023academic year） Year-round  - その他

  • Advanced Mathematical Science in Liberal Arts （2023academic year） Third semester  - 水3～4

  • Special Research （2023academic year） Year-round  - その他

  • Advanced Study （2023academic year） Other  - その他

  • Linear Algebra III-1 （2023academic year） special  - その他

  • Linear Algebra 1 （2023academic year） Third semester  - 月7～8

  • Linear Algebra 2 （2023academic year） Fourth semester  - 月7～8

  • Introduction to Discrete Mathematics （2023academic year） Fourth semester  - 月1～2,木1～2

  • Introduction to Discrete Mathematics 1 （2023academic year） Fourth semester  - 月1,木1

  • Introduction to Discrete Mathematics 2 （2023academic year） Fourth semester  - 月2,木2

  • Foundation of Algebra 1 （2022academic year） special  - その他

  • Foundation of Algebra 2 （2022academic year） special  - その他

  • Keys in Algebra 1 （2022academic year） 1st semester  - 月5～6

  • Keys in Algebra 2 （2022academic year） Second semester  - 月5～6

  • Topics in Commutative Algebra （2022academic year） Prophase  - その他

  • Seminar on Applied Mathematics （2022academic year） Prophase  - その他

  • Seminar in Applied Mathematics （2022academic year） Late  - その他

  • Seminar on Applied Mathematics （2022academic year） Late  - その他

  • Seminar in Applied Mathematics （2022academic year） Prophase  - その他

  • Applied Computational Algebra （2022academic year） Late  - 木3～4

  • Advanced Mathematical Science in Liberal Arts （2022academic year） Third semester  - 月5～6

  • Glance at Mathematical Science A （2022academic year） Second semester  - 金5～6

  • Special Research （2022academic year） Year-round  - その他

  • Linear Algebra 1 （2022academic year） Third semester  - 月7～8

  • Linear Algebra 2 （2022academic year） Fourth semester  - 月7～8

  • Introduction to Discrete Mathematics （2022academic year） Fourth semester  - 月3～4,木1～2

  • Introduction to Discrete Mathematics 1 （2022academic year） Fourth semester  - 月3,木1

  • Introduction to Discrete Mathematics 2 （2022academic year） Fourth semester  - 月4,木2

  • Seminar on Foundation of Mathematical Science （2021academic year） Third semester  - 月1,月2

  • Foundation of Algebra 1 （2021academic year） Third semester  - 木7～8

  • Foundation of Algebra 2 （2021academic year） Fourth semester  - 木7～8

  • Keys in Algebra 1 （2021academic year） 1st semester  - 月5～6

  • Keys in Algebra 2 （2021academic year） Second semester  - 月5～6

  • Algebra I （2021academic year） 3rd and 4th semester  - 木7～8

  • AlgebraⅡ （2021academic year） 1st and 2nd semester  - 月5～6

  • Introduction to Commutative Algebra （2021academic year） Late  - 月5～6

  • Topics in Commutative Algebra （2021academic year） Prophase  - その他

  • Seminar on Foundation of Mathematical Science （2021academic year） Third semester  - 月1～2

  • Seminar on Applied Mathematics （2021academic year） Prophase  - その他

  • Seminar in Applied Mathematics （2021academic year） Late  - その他

  • Seminar on Applied Mathematics （2021academic year） Late  - その他

  • Seminar in Applied Mathematics （2021academic year） Prophase  - その他

  • Special Research （2021academic year） Year-round  - その他

  • Introduction to Discrete Mathematics （2021academic year） 1st and 2nd semester  - 月7,月7～8

  • Introduction to Discrete Mathematics 1 （2021academic year） 1st semester  - 月7～8

  • Introduction to Discrete Mathematics 2 （2021academic year） Second semester  - 月7～8

  • Foundation of Algebra 1 （2020academic year） Third semester  - 木6,木7

  • Foundation of Algebra 2 （2020academic year） Fourth semester  - 木6,木7

  • Keys in Algebra 1 （2020academic year） 1st semester  - 月4,月5

  • Keys in Algebra 2 （2020academic year） Second semester  - 月4,月5

  • Algebra I （2020academic year） 3rd and 4th semester  - 木6,木7

  • AlgebraⅡ （2020academic year） 1st and 2nd semester  - 月4,月5

  • Topics in Commutative Algebra （2020academic year） special  - その他

  • Calculus 1 （2020academic year） Third semester  - 木3,木4

  • Seminar in Applied Mathematics （2020academic year） Late  - その他

  • Seminar on Applied Mathematics （2020academic year） Prophase  - その他

  • Seminar in Applied Mathematics （2020academic year） Prophase  - その他

  • Seminar on Applied Mathematics （2020academic year） Late  - その他

  • Applied Computational Algebra （2020academic year） Late  - 月2,月3

  • Advanced Mathematical Science in Liberal Arts （2020academic year） Third semester  - 月6,月7

  • Special Research （2020academic year） Year-round  - その他

  • Introduction to Discrete Mathematics （2020academic year） 1st and 2nd semester  - 月6,月7

  • Introduction to Discrete Mathematics 1 （2020academic year） 1st semester  - 月6,月7

  • Introduction to Discrete Mathematics 2 （2020academic year） Second semester  - 月6,月7

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