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1. Logic
2. Linear Equations
3. Quadratic Equations
4. Graphs and Functions
5. Differentiation
6. Unconstrained optimization
7. Partial differentiation
8. Constrained optimization
9. Integration
10. Geometric series
11. Difference equations (optional)
12. Differential equations (optional)
13. Matrix algebra (optional)
个人认为作为一名能考上港大的高考理科生，这门课的内容太过简单，可不上，直接上MATH1013。
但是如果为了刷GPA，且你是一个很仔细做简单题不容易错的人，也可以考虑上这门课。
我没有上过这门课所以不过多评价。
II. MATH1013 University math II
课程内容：
- Functions; graphs; inverse functions.
- Limits; continuity and differentiability.
- Mean value theorem; Taylor's theorem; implicit differentiation; L'Hopital's rule.
- Higher order derivatives; maxima and minima; graph sketching.
- Radian, calculus of trigonometric functions.
- Definite and indefinite integrals; integration by substitutions; integration by parts; integration by partial fractions.
- Complex numbers, polar form, de Moivre's formula.
- Applications: Solving simple ordinary differential equations.
- Basic matrix and vector (of orders 2 and 3) operations, determinants of 2x2 or 3x3 matrices.
这门课是选择后面很多高阶课的前置课程，所以在理科生在大一上掉这门课个人感觉还是挺不错的。
考评方式：
Assignment 10%
Exam 50%
Test 40%
Professor测评：Ching Tak Wing
这名教授是我大一遇到讲课好的老师之一，他讲课逻辑非常清晰，而且是真的为数不多的 只要跟着他的逻辑走 就可以把你从不会讲成会的大学老师。每次lecture他都会录制，一下课就会上传给我们看。整个学期他都在forum上答疑，下课后也可以抓着他讨论问题，而且他回邮件非常快。每次考试前的晚上他都会在线解同学们的燃眉之急。
Tutor测评：
上学年一学期，这门课的tutor整体质量真的很差。因为tutorial不需要记attendance，所以我为了找到一个相对好一点的tutor辗转换了三个tutorial subclass。如果你开学后发现自己的tutor教的不好也可以这样做，翘课翘掉自己的tutorial然后去其他你有空的时间段去试试。相对于lecture materials，总的来说我觉得我并没有很好地吸收tutorial上的东西，但是也不是很影响这门课的成绩。
内容测评：
这门课内容相对简单，高考理科生可以直接上无负担。最开始两章是高中学过的内容，更多地是在适应用英文学数学。然后讲了三章calculus，有些是高中学过的有些是新东西诸如积分、微积分基本定理等。最后两章是全新的ODE，matrix。因为过渡得宜且教授专业水平过硬，能够顺滑跟上，而且不需要很累心，只需要上课理解了并把课后作业写完就能很很有收获了。弱tutor在强professor面前是可以忽略的缺点。
考评方式：这门课有两个test和一个final，平时有四五个手写的Assignment和一些网上可无限作答刷正确率的quiz，属于典型的hku数学课配置。
成绩：普遍好龟，努力了能有A range，教授也会捞人。
workload：⭐️⭐️⭐️🌛/⭐️⭐️⭐️⭐️⭐️
III. MATH1851 Calculus and ordinary differential equations
课程内容：
- Differential and integral calculus (single variable) [limits and continuity, derivatives, (higher-order) derivatives of elementary functions, derivatives by implicit differentiation, the mean value theorem, L'H\^{o}pital's rule, parametric representation of curves, polar coordinates, indefinite integrals, integration by parts, partial fractions decomposition, definite integrals, the fundamental theorem of calculus, and their applications]
- Ordinary differential equations [first order equations, integrating factors and linear equations, Bernoulli equations, separable equations, homogeneous equations, exact differential equations, higher-order homogeneous linear equations with constant coefficients, characteristic polynomials, methods of undetermined coefficients and variation of parameters, higher-order inhomogeneous linear ordinary differential equations, choice of particular solutions and physical implication of resonance, Cauchy-Euler equations, and their applications]
- Laplace transforms [Laplace transforms of elementary functions, inverse Laplace transforms, transforms of derivatives and integrals, derivatives of Laplace transform, first and second shifting theorems, convolutions, partial fractions, solution of linear differential equations (initial value problems) using Laplace transforms]
这门课是数学系专门为工程学院BEng学生开的数学课。除了特定学生群体，其他人都选不了。很遗憾我也没上过这门课，无法给出具体评价。
IV. MATH1853 Linear Algebra, Probability and Statistics
课程内容：
- Linear algebra [vectors and scalars, inner product, vector projection, linear dependence and independence, matrix, determinant, matrix inverse, system of linear equations, matrix equation, Gaussian elimination, Cramer's rule, matrix rank, eigenvalue, eigenvector, matrix diagonalization, positive, negative and semi-definiteness, and their applications]
- Elementary complex variables [arithmetics of complex numbers, representations of complex numbers, De Moivre's theorem, roots of unity, complex functions, and their applications]
- Basic probability theory [axioms of probability, conditional probability, Bayes' theorem, the total probability formula, random variable, (joint) probability distribution, expectation, variance, independence, and their applications]
- Commonly used distributions [Bernoulli, Binomial, Geometric, Negative Binomial, Exponential, Poisson and Normal distribution, and their applications]
- Basic statistics [point estimates, sample mean, sample variance with known or unknown mean, confidence interval for a population mean with known or unknown population variances, inference for proportion, and their applications]
