美國(guó)本科大多數(shù)專業(yè)都會(huì)要求至少要修“數(shù)學(xué)或計(jì)算機(jī)（在BU叫MCS）”兩門基礎(chǔ)課。以下CAS是文理學(xué)院的意思。MA XXX 是課程代號(hào)。更加具體的課程的設(shè)置同學(xué)們可以去學(xué)校的官網(wǎng)自己查詢哈~如果同學(xué)們有美國(guó)大學(xué)本科基礎(chǔ)數(shù)學(xué)的輔導(dǎo)需求，可以聯(lián)系我們的客服老師，教務(wù)部會(huì)同步海外課程，幫助學(xué)生進(jìn)行輔導(dǎo)學(xué)習(xí)的。

CAS MA 107: Mathematical Reasoning in the Elementary Grades: Number Systems

Mathematical Reasoning in the Elementary Grades: Number Systems Required for undergraduates seeking licensure in elementary education,early childhood education,special education,or deaf studies. Focuses on number systems,whole number,decimal and fraction concepts and operations,and number theory. Non-Wheelock students by signed permission only.Does not satisfy CAS Divisional Studies or Math/Stat major.

CAS MA 108: Mathematical Reasoning in the Elementary Grades: Algebra,Geometry,and Statistics

Undergraduate prerequisites: CAS MA 107 or SED ME 503.

Required for undergraduates seeking licensure in elementary education,special education,or deaf studies. Focuses on topics in algebra,geometry,measurement,and statistics. Non-SED students by signed permission only. Does not satisfy CAS Divisional Studies or Math/Stat major.

以上這兩門課太基礎(chǔ)了，所以連學(xué)校兩門數(shù)學(xué)基礎(chǔ)課的標(biāo)準(zhǔn)都達(dá)不了，所以要選這兩門只能是以興趣來上這門課，拿普通的學(xué)分。內(nèi)容大致接近美高12年級(jí)的內(nèi)容。

CAS MA 109: The Art and Science of Quantitative Reasoning

Buying music on-line,making phone calls,predicting the weather,or controlling disease outbreaks would be impossible without mathematics,statistics,and computer science. Focuses on methods of reasoning common to these disciplines,and how they enable the modern world. Also offered as CAS CS 109. Carries MCS divisional credit in CAS.

CAS MA 111: Mathematical Explorations

Students explore challenging mathematics problems chosen from an array of topics that can be solved in multiple ways. Includes making,testing,and modifying conjectures; constructing proofs; posing new problems; extensive classroom interaction; reflective and other writing.

CAS MA 113: Elementary Statistics

CAS MA 113 may not be taken for credit by any student who has completed any MA course numbered 300 or higher. Students may receive credit for not more than one of the following courses: CAS MA 113,MA 115,or MA 213. Basic concepts of estimation and tests of hypotheses,ideas from probability; one-,two-,and multiple-sample problems. Applications will be in social sciences and students will be able to answer understand the basics of using a sample to predict uncertainty. Carries MCS divisional credit in CAS.

CAS MA 115: Statistics I

CAS MA 115 may not be taken for credit by any student who has completed any MA course numbered 300 or higher. Students may receive credit for not more than one of the following courses: CAS MA 113,MA 115,or MA 213. Numerical and graphical summaries of univariate and bivariate data. Basic probability,random variables,binomial distribution,normal distribution. One- sample statistical inference for normal means and binomial probabilities. primarily for students in the social sciences with limited mathematics preparation. Carries MCS divisional credit in CAS.

CAS MA 116: Statistics II

Undergraduate prerequisites: CAS MA 115; or equivalent.

CAS MA 116 may not be taken for credit by any student who has completed any MA course numbered 300 or higher. Students may receive credit for not more than one of the following courses: CAS MA 116,MA 214,or MA 614. This course introduces basic statistical modeling techniques. One- or two- sample inference for unknown means,proportions and variances,categorical data analysis,introduction to design of experiments and analysis of variance,analysis of simple and multiple linear regression models,non-parametric methods. Carries MCS divisional credit in CAS.

CAS MA 118: College Algebra and Trigonometry

MA 118 may not be taken for credit by any student who has completed any MA course numbered 121 or higher. Functions and graphs. Linear and quadratic equations. Exponents; logarithms. Right and oblique triangles; trigonometric functions. Optimization. Specifically intended to prepare students with insufficient background in mathematics for the study of calculus. This course may not be used in fulfillment of the divisional studies requirement. Satisfies the mathematics requirement in the College program.

CAS MA 119: Applied Mathematics for personal Finance

Applications of mathematics for personal financial decision-making. Systems of equations,exponential functions,logarithms,probability,descriptive statistics,and numerical simulation,for modeling saving,borrowing,inflation,purchasing power,taxation,government benefits,risk management,insurance,annuities,and investments. Carries MCS divisional credit in CAS.

CAS MA 120: Applied Mathematics for Social and Management Sciences

MA 120 may not be taken for credit by any student who has completed any MA course numbered 124 or higher. Topics chosen from Linear equations,systems of linear equations,matrix algebra,exponential functions and logarithms,elements of differential calculus,optimization,probability. Some sections focus on applications in economics,finance,and management. Satisfies both mathematics requirement and divisional studies requirement. Carries MCS divisional credit in CAS.

CAS MA 121: Calculus for the Life and Social Sciences I

Students may receive credit for not more than one of the following courses: CAS MA 121 or CAS MA 123. Differentiation and integration of functions of one variable. Same topics as CAS MA 123,but with less emphasis on mathematical generality and more on applications. Especially suitable for students concentrating in the biological and social sciences. Carries MCS Divisional credit in CAS.

CAS MA 122: Calculus for the Life and Social Sciences II

Undergraduate prerequisites: CAS MA 121 or CAS MA 123.

Students may receive credit for not more than one of the following courses: CAS MA 122,MA 124,MA 127 or MA 129. Continuation of CAS MA 121. Review of univariate calculus,calculus of the elementary transcendental functions,elementary differential equations,elementary multivariate calculus. Applications to exponential growth,optimization,equilibrium,and dynamic modeling problems. Carries MCS divisional credit in CAS.

這以上的課程在后面如果加上了Carries MCS divisional credit in CAS,那就是學(xué)校認(rèn)可的符合標(biāo)準(zhǔn)的課程，可以當(dāng)做兩門之一來選。沒有寫的是符合了BU另外一個(gè)通識(shí)課標(biāo)準(zhǔn)體系，不過大多數(shù)學(xué)生走的是第一個(gè)體系。

在這里面的課程，其實(shí)是非常豐富多彩的。對(duì)于非數(shù)學(xué)專業(yè)的美國(guó)人來講，難度看個(gè)人水平，我曾經(jīng)當(dāng)過以上兩門課的Grader，基本上都是老美上，考試難度也沒有太離譜，老師基本上都算仁慈。對(duì)于中國(guó)人來講基本上是秒殺課，不拿A有點(diǎn)說不過去。

如果你是數(shù)學(xué)系或者是理工科的學(xué)生，以上的所有課程是沒有必要修的，真正基礎(chǔ)課是從下面開始的。

CAS MA 123: Calculus I

Students may receive credit for not more than one of the following courses: CAS MA 121 or CAS MA 123. Limits; derivatives; differentiation of algebraic and transcendental functions. Applications to maxima,minima,and convexity of functions. The definite integral; the fundamental theorem of integral calculus. Carries MCS divisional credit in CAS.

這門課就是微積分1，基本上80%的中國(guó)學(xué)生都要修，且目標(biāo)都是A，如果你在國(guó)內(nèi)讀完了普高體系，這門課基本上就是復(fù)習(xí)課。

CAS MA 124: Calculus II

Undergraduate prerequisites: CAS MA 121 or CAS MA 123.

Students may receive credit for not more than one of the following courses: CAS MA 122,MA 124,MA 127,or MA 129. Logarithmic,exponential,and trigonometric functions. Sequences and series; Taylor's series with the remainder. Methods of integration. Calculus I and II together constitute an introduction to calculus of a function of a single real variable. Carries MCS divisional credit in CAS.

這門課是微積分2，銜接了微積分1的內(nèi)容，對(duì)于數(shù)學(xué)專業(yè)的同學(xué)來講，也必須是個(gè)輕松搞定的課，如果在這里感覺難，可以適當(dāng)考慮換專業(yè)了。

CAS MA 150: Investigations in Geometry

An immersion experience in mathematical thinking and mathematical habits of mind. Students investigate topics in Euclidean and non-Euclidean geometry starting from basic elementary material and leading to an overview of current research topics. Does not satisfy MCS Divisional requirement. Does satisfy CAS WR 150 requirement.

這門課很有趣，因?yàn)槊辣疽罅?-4門必修的寫作課，這門課可以當(dāng)做數(shù)學(xué)cross寫作的一門課，既能滿足修數(shù)學(xué)的一個(gè)學(xué)分，也能滿足寫作最高階的那門課。這里就展示出來美本選課的多樣性。

CAS MA 193: Discrete Mathematics for Engineering

propositional logic,set theory,relations,combinatorics,graphs. Topics are treated with particular emphasis on applications to the engineering discipline. (Cannot be taken for credit in addition to CAS MA 293.)

這門課基本上是給工學(xué)院的同學(xué)上的，數(shù)學(xué)系的同學(xué)很少修這門課，這也展示出了數(shù)學(xué)系的課程其實(shí)是支撐了整個(gè)理工體系的基礎(chǔ)課。

CAS MA 213: Basic Statistics and probability

Undergraduate prerequisites: good background in high school algebra.

Students may receive credit for not more than one of the following courses: CAS MA 113,MA 115,or MA 213. Elementary treatment of probability densities,means,variances,correlation,independence,the central limit theorem,confidence intervals,and p-values. Students will be able to answer questions such as how can a pollster use a sample to predict the uncertainty of an election? Carries MCS divisional credit in CAS.

這門課是統(tǒng)計(jì)的第一門專業(yè)基礎(chǔ)課，除了數(shù)學(xué)系的同學(xué)上之外，很多商學(xué)院的人會(huì)來修這門課，畢竟內(nèi)容是和商業(yè)分析直接相關(guān)的。

CAS MA 214: Applied Statistics

Undergraduate prerequisites: CAS MA 213; or consent of instructor.

Students may receive credit for not more than one of the following courses: CAS MA 116,MA 214,or MA 614. Inference about proportions,goodness of fit,student's t-distribution,tests for normality; two-sample comparisons,regression and correlation,tests for linearity and outliers,residual analysis,contingency tables,analysis of variance. Carries MCS divisional credit in CAS.

這是統(tǒng)計(jì)專業(yè)的第二門專業(yè)課，延續(xù)了統(tǒng)計(jì)1，這門課上完之后呢，大家就要開始選擇自己的方向了，到底是走純數(shù)學(xué)和應(yīng)用數(shù)學(xué)的道路，還是走統(tǒng)計(jì)的道路了。大多數(shù)的非數(shù)學(xué)專業(yè)的理科學(xué)生在數(shù)學(xué)的學(xué)習(xí)內(nèi)容就止步于此了，一些工科學(xué)生還要繼續(xù)修多變量微積分和線性代數(shù)。

以上便是美國(guó)大學(xué)本科基礎(chǔ)數(shù)學(xué)會(huì)學(xué)習(xí)到的一些課程，基礎(chǔ)數(shù)學(xué)難度相對(duì)較低，如果有基礎(chǔ)不好的同學(xué)在學(xué)習(xí)中遇到問題一定要盡快補(bǔ)習(xí)，知識(shí)的補(bǔ)充和更新一定要快，數(shù)學(xué)是一門很有邏輯很多思維的課程，找到對(duì)的學(xué)習(xí)方法會(huì)事半功倍。