This document is a seminar note on singular homology.<\/p>\n
Before reading this article, make sure you have known the Chapter 1-3 of An Introduction to Algebraic Topology<\/em>, written by Rotman.<\/p>\nYou can download the pdf version from this link<\/a>.<\/p>\nReference<\/strong><\/p>\n\nAn Introduction to Algebraic Topology<\/em>, Rotman<\/li>\nTopology and Geometry<\/em>, Bredon <\/li>\n\u4ee3\u6570\u5b66\u65b9\u6cd5 \u5377\u4e00\uff1a\u57fa\u7840\u67b6\u6784<\/em>, \u674e\u6587\u5a01<\/li>\nnlab<\/a><\/li>\n\n<\/ul>\nWhy should we learn homology?<\/strong><\/p>\nWhen we use calculus to solve physical problems, we often encounter functions like<\/p>\n<\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/defs><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/g><\/g><\/g><\/rect><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/g><\/svg><\/mjx-container><\/div><\/div>\nwhere <\/path><\/path><\/path><\/defs><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/g><\/svg><\/mjx-container>
You can download the pdf version from this link<\/a>.<\/p>\nReference<\/strong><\/p>\n\nAn Introduction to Algebraic Topology<\/em>, Rotman<\/li>\nTopology and Geometry<\/em>, Bredon <\/li>\n\u4ee3\u6570\u5b66\u65b9\u6cd5 \u5377\u4e00\uff1a\u57fa\u7840\u67b6\u6784<\/em>, \u674e\u6587\u5a01<\/li>\nnlab<\/a><\/li>\n\n<\/ul>\nWhy should we learn homology?<\/strong><\/p>\nWhen we use calculus to solve physical problems, we often encounter functions like<\/p>\n<\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/defs><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/g><\/g><\/g><\/rect><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/g><\/svg><\/mjx-container><\/div><\/div>\nwhere <\/path><\/path><\/path><\/defs><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/g><\/svg><\/mjx-container>
Reference<\/strong><\/p>\n\nAn Introduction to Algebraic Topology<\/em>, Rotman<\/li>\nTopology and Geometry<\/em>, Bredon <\/li>\n\u4ee3\u6570\u5b66\u65b9\u6cd5 \u5377\u4e00\uff1a\u57fa\u7840\u67b6\u6784<\/em>, \u674e\u6587\u5a01<\/li>\nnlab<\/a><\/li>\n\n<\/ul>\nWhy should we learn homology?<\/strong><\/p>\nWhen we use calculus to solve physical problems, we often encounter functions like<\/p>\n<\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/defs><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/g><\/g><\/g><\/rect><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/g><\/svg><\/mjx-container><\/div><\/div>\nwhere <\/path><\/path><\/path><\/defs><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/g><\/svg><\/mjx-container>
Why should we learn homology?<\/strong><\/p>\nWhen we use calculus to solve physical problems, we often encounter functions like<\/p>\n<\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/defs><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/use><\/g><\/g><\/g><\/g><\/rect><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/g><\/svg><\/mjx-container><\/div><\/div>\nwhere <\/path><\/path><\/path><\/defs><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/g><\/svg><\/mjx-container>
When we use calculus to solve physical problems, we often encounter functions like<\/p>\n
where <\/path><\/path><\/path><\/defs><\/use><\/g><\/use><\/g><\/use><\/g><\/g><\/g><\/svg><\/mjx-container>