本周二下午，加拿大滑铁卢大学教授 Paul McGrath 先生莅临我校 BC 课程部，举办了一场以“探索生活中的数学-解密数学的奥秘”为主题的讲座。在讲座过程中，Paul McGrath 先生也和同学们进行了有趣有序的互动，吸引了众多师生热情参与。
On Tuesday afternoon, Mr. Paul McGrath, a professor from the University of Waterloo in Canada, visited the BC department and held a lecture themed “Exploring Mathematics in Life – Unraveling the Mysteries of Mathematics”. During the lecture, Mr. Paul McGrath also had interesting and orderly interactions with the students, attracting the enthusiastic participation of many teachers and students.
讲座伊始，Paul McGrath便以一道经典的逻辑推理题 “Flipping Cards”（翻转卡片问题）点燃了现场气氛。题目围绕验证命题 “如果一张卡片上是小写字母，则其背面是奇数” 展开，学生们需要思考最少翻转哪些卡片来证明命题正确性。这一问题巧妙考察了数学中的命题逻辑与归谬法，促使学生们全方位思考，现场踊跃作答，气氛热烈非凡。
At the beginning of the lecture, Paul McGrath ignited the atmosphere with a classic logical reasoning problem, “Flipping Cards”. The problem revolved around verifying the proposition “If a card has a lowercase letter on one side, then the number on the other side is odd”. Students needed to think about which cards to flip at a minimum to prove the correctness of the proposition. This problem ingeniously examined the propositional logic and reductio ad absurdum in mathematics, prompting students to think comprehensively. The students actively answered questions on the spot, and the atmosphere was extremely enthusiastic.
紧接着，极具挑战性的 “8×8 国际象棋棋盘覆盖问题” 来袭。去掉对角线上两个黑色方格后，能否用31个骨牌铺满棋盘？在学生们积极尝试构造解法的过程中，老师揭示了问题关键：因骨牌需覆盖一黑一白格子，而移除同色方格后棋盘黑白数量失衡，无法实现覆盖。这让大家对数学中的构造与反证法有了更为深刻的理解。
Immediately following the first logical reasoning problem, the highly challenging “8×8 chessboard covering problem” emerged. After removing two black squares on the diagonal, can 31 dominoes be used to cover the chessboard? During the process when students actively tried to construct solutions, the teacher revealed the key to the problem: since dominoes need to cover one black and one white square, and after removing squares of the same color, the number of black and white squares on the chessboard is unbalanced, making it impossible to achieve coverage. This enabled everyone to have a deeper understanding of construction and proof by contradiction in mathematics.
在讲座后半部分，McGrath 老师详细介绍了滑铁卢数学竞赛的特点、评分标准以及备考建议。他着重指出，该竞赛并非仅关注计算能力，更看重解题思维与过程表达，对有志于申请数学、计算机及工程类专业的学生意义重大。老师还贴心给出备赛建议，鼓励同学们研究往届试题熟悉题型难度，善用 CEMC 备考资源如 Problem Set Generator，定期开展模拟训练提升应试能力。
In the second half of the lecture, Mr. McGrath introduced in detail the characteristics, scoring criteria, and preparation suggestions for the Waterloo Mathematics Competition. He emphasized that this competition does not only focus on computational ability but also attaches great importance to problem-solving thinking and process expression, which is of great significance for students who apply for majors in mathematics, computer science, and engineering. The teacher also thoughtfully provided preparation suggestions, encouraging students to study past exam questions to get familiar with the question types and difficulty levels, make good use of CEMC preparation resources such as the Problem Set Generator, and regularly conduct simulation training to improve their test-taking abilities.
此次讲座不仅带领同学们发现生活中的数学知识，更激发了大家对数学思维的深入探索。期待同学们在未来竞赛中展现风采，收获佳绩！
This lecture not only led students to discover mathematical knowledge in life but also inspired everyone to conduct an in-depth exploration of mathematical thinking. We look forward to seeing students showcase their talents and achieve excellent results in future competitions!
讲座结束后，BC课程部校长Toni Wereschuk女士，为Paul McGrath先生颁发了荣誉讲师证书。
10D Leo：
我觉得今天的讲座安排得非常好，我也获得了一些关于未来选课和相关学校的有价值信息。我对数学非常感兴趣，去年也参加了滑铁卢数学竞赛，并进入前25%。今年4月份的滑铁卢数学竞赛我也报名了，希望可以取得更好得成绩。关于未来专业的选择我也有过思考，大体方向应该是数学偏物理，同时我也参加了一些关于机器人和工程方面的活动，希望自己多尝试，找到自己真正喜爱的、擅长的又可以与未来就业紧密相连的发展方向。
I think today’s lecture was very well – arranged, and I obtained some valuable information about future course selection and related schools. I am very interested in mathematics. Last year, I participated in the Waterloo Mathematics Competition and ranked in the top 25%. I have also signed up for the Waterloo Mathematics Competition in April this year and hope to achieve better results. I have also thought about my future major selection. The general direction should be mathematics with a focus on physics. At the same time, I have participated in some activities related to robotics and engineering, hoping to try more and find a development direction that I truly love, am good at, and that is closely related to future employment.
11A Sophia：
听完滑铁卢大学教授的讲座后，我受益匪浅。虽然我未来的专业是生物，但数学在生物学中的应用越来越广泛。讲座让我意识到，数学不仅仅是工具，更是一种思维方式，遇到困难时能够帮助我更好地理解、分析并解决。我参加过几次滑铁卢数学竞赛，也拿过奖，在此过程中我的逻辑思维能力得到了提升，也让我更加欣赏数学的美妙。未来，我希望能够将数学与生物学更紧密地结合，探索更多跨学科的可能性。
After listening to the lecture by the professor from the University of Waterloo, I have benefited a great deal. Although my future major is biology, the application of mathematics in biology is becoming increasingly widespread. The lecture made me realize that mathematics is not only a tool but also a way of thinking that can help me better understand, analyze, and solve problems when faced with difficulties. I have participated in the Waterloo Mathematics Competition several times and won awards. During this process, my logical thinking ability has been improved, and I have come to appreciate the beauty of mathematics even more. In the future, I hope to combine mathematics and biology more closely and explore more interdisciplinary possibilities.
12A Jasmine ：
老师讲的很有趣，讲了一些逻辑的问题，不同数学水平的人都可以参与，也从这些问题延伸到更专业的数学领域，比如证明的方法。数学和我想学习的工程专业相关性很高，这个讲座也让我对数学更感兴趣了，它可以帮我解决很多有趣的问题。
The teacher’s lecture was very interesting. He talked about some logical problems that people with different mathematical levels could participate in, and also extended these problems to more professional mathematical fields, such as proof methods. Mathematics is highly relevant to the engineering major I want to study. This lecture has also made me more interested in mathematics as it can help me solve many interesting problems.
12C Harry：
我觉得这次讲座上的内容并不全是数学，更倾向于是一种逻辑思维上的锻炼，可能是为了以后大学层面的更高级数学做一些铺垫。通过教授展示的几个小题目，我对数学的兴趣又浓厚了几分，感觉数学不再是一个很抽象的，遥远的东西，也能通过某种方式进入到我们的日常生活里。我感谢学校能请到这样一位教授来启发我们对数学的兴趣，这次经历不仅让我对数学产生了更近一步的理解，也通过和这位教授的互动，对未来的大学生活有了更多的期待。
I don’t think all the content in this lecture was about mathematics. It was more of an exercise in logical thinking, perhaps paving the way for more advanced mathematics at the university level. Through the few small problems demonstrated by the professor, my interest in mathematics has grown even stronger. I feel that mathematics is no longer an abstract and distant thing, but can also enter our daily lives in a certain way. I am grateful to the school for inviting such a professor to inspire our interest in mathematics. This experience has not only given me a deeper understanding of mathematics but also, through interactions with this professor, made me look forward more to my future college life.
