Hermann weyl " , , " in these days the angel of topology and the devil of abstract algebra fight for the soul of each individual matehmatical domain . " , 在這些日子里,拓?fù)溥@個(gè)天使和抽象代數(shù)這個(gè)魔鬼為各自占有每一塊數(shù)學(xué)領(lǐng)域而斗爭(zhēng)著.
Apos theory relatively prevails abroad at present and it has already been widely used in many aspects , such as function concept , abstract algebra , dispersed mathematics , calculus 目前apos理論在國(guó)外比較盛行,已經(jīng)在函數(shù)概念、抽象代數(shù)、離散數(shù)學(xué)、微積分等多方面領(lǐng)域得到廣泛應(yīng)用。
In the area of pure mathematics , topics include number theory , abstract algebra , real and complex analysis , functional analysis , differential geometry , topology , and differential equations 在純數(shù)學(xué)的范疇,可供選讀的科目包括數(shù)論、抽象代數(shù)、實(shí)和復(fù)分析、泛函分析、微分幾何、拓?fù)鋵W(xué)及微分方程理論等。
The first part , the theory and application about wu - ritt differential characteristic sequence method are discussed , which involves the theories of differential equations , abstract algebra and computer algebra etc . we apply wu - ritt differential characteristic sequence method ( abbr . wu - ritt method ) to linear partial differential equations which has physics significance and give the size of solutions and formal taylor solutions 本文共分兩部分,第一部分討論微分特征列法的理論和應(yīng)用問(wèn)題,涉及到微分方程,抽象代數(shù),計(jì)算機(jī)代數(shù)等重要學(xué)科。將吳方法應(yīng)用到具有物理意義的線性偏微分方程上去,我們給出了型序,驗(yàn)證了張鴻慶教授八十年代給出的恰當(dāng)解的概念,刻劃了解的規(guī)模并給出了形式冪級(jí)數(shù)解。
Based on the course of " abstract algebra " , this paper aims to discuss how to develop students ' mathematical ability and interests and how to implement the education for all - round development from the following four sides : " establishing algebraic system , studying algebraic system , differentiating algebraic system and using algebraic system " 摘要從“抽象代數(shù)”課程的角度,圍繞“建立代數(shù)體系、研究代數(shù)體系、區(qū)分代數(shù)體系、應(yīng)用代數(shù)體系”四個(gè)方面,討論教學(xué)過(guò)程中如何培養(yǎng)學(xué)生的數(shù)學(xué)能力和數(shù)學(xué)素質(zhì),如何實(shí)施素質(zhì)教育。
In this article , we study the implemetation of fpga for elliptic curve digital signature algorithm . based on number thesis 、 abstract algebra and complex thesis , integrated information theory 、 cryptography and some specific relevant algorithm , we ascertain the implementation of ecdsa for hardware project : according to the design idea of hiberarchy and modularization , we adopt very high speed ic hardware description language ( vhdl ) as design input and simulate the design in every level and every model for the correct of the fundamental design . after finish the top design , we perform the whole simulation . then , we carry out the timing simulation after the logic synthes and layout 本文從實(shí)際應(yīng)用出發(fā),研究了橢圓曲線數(shù)字簽名算法的fpga的實(shí)現(xiàn):以基本的數(shù)論理論、抽象代數(shù)和復(fù)雜度理論為依據(jù),結(jié)合信息論、密碼學(xué)的一些知識(shí)以及一些具體的相關(guān)算法,確定了ecdsa的硬件實(shí)現(xiàn)方案:按照層次化、模塊化的設(shè)計(jì)思想,采用硬件描述語(yǔ)言vhdl作為設(shè)計(jì)輸入進(jìn)行ecdsa的硬件設(shè)計(jì);在每個(gè)設(shè)計(jì)層次和每個(gè)模塊都進(jìn)行了仿真驗(yàn)證,得以保證底層設(shè)計(jì)的正確性。在確保每個(gè)模塊的設(shè)計(jì)正確后,完成對(duì)電路的頂層設(shè)計(jì),進(jìn)行總體的仿真。
百科解釋
In algebra, which is a broad division of mathematics, abstract algebra is a usual name for the sub-area that studies for themselves algebraic structures such as groups, rings, fields, modules, vector spaces, and algebras. The term abstract algebra was coined at the turn of the 20th century to distinguish this area from the other parts of algebra.