高等代数知识在初等数学中的应用本科生毕业（设计）论文.doc

本 科 生 毕 业 论 文 高等代数知识在初等数学中的应用 目 录 摘要 I Abstract II 第一章 绪论 1 第二章 高等代数与初等数学的联系 2 2.1知识方面的区别与联系 2 2.2思想方法方面的区别与联系 2 2.3观念方面的区别与联系 4 第三章 多项式理论在初等数学中的应用 5 3.1去重因式分解多项式 5 3.2 利用因数定理分解多项式 5 3.3利用对称多项式与轮换多项式的性质分解多项式 6 3.4多项式的一些应用 6 第四章 行列式在初等数学中的应用 8 4.1应用行列式判定二元二次多项式的可分解性 8 4.2应用行列式分解因式 9 4.3应用行列式解决数列问题 9 第五章 线性方程组在初等数学中的应用 12 5.1 在平面解析几何上的应用 12 5.2在空间解析几何中的应用 13 5.3在求解二元方程组上的应用 14 第六章 柯西不等式在初等数学中的应用 15 6.1柯西不等式在解析几何中的应用 15 6.2柯西不等式在解其它题方面的应用 15 第七章 结 论 18 参考文献 19 致谢 20 摘 要 高等代数在初等代数的基础上研究对象进一步的扩充高等代数是初等的进化高等代数不仅是初等数学的延拓，也是现代数学的基础，只有很好的掌握高等代数的基础知识才能适应数学发展和教材改革高等代数知识在开阔视野，指导中学解题等方面的作用尤为突出 Abstract Higher algebra is an important branch of modern mathematics, which is on the basis of the elementary algebra research object for further expansion. Advanced algebra is the evolution of elementary mathematics. Advanced algebra is not only the continuation of elementary mathematics, also is the foundation of modern mathematics, only good to master the basic knowledge of advanced algebra can adapt the mathematical development and teaching materials reform. Advanced algebra in the open field of vision of knowledge, especially the role of guiding middle school problem solving, etc. In many problems, if we can use the advanced algebra knowledge to solve some problems in the elementary mathematics, converting the proposition to general problems are solved, can often get twice the result with half the effort, make the person find everything new and fresh. Higher algebra and elementary mathematics were introduced on the one hand, from the concept of mathematics knowledge, mathematics thought method, mathematics three aspects of excavating the higher mathematics curriculum links with the middle school mathematics. On the other hand, introduces some knowledge of advanced algebra in the application of elementary mathematics. Such as polynomial, determinant, system of linear equations, cauchy inequality in elementary mathematics, the application of ad