KTH Royal Institute of Technology
MSc Applied and Computational Mathematics
Stockholm, 瑞典
期间
2 Years
语言
英语
步伐
全职
报名截止日期
Request application deadline
最早开始日期
Aug 2024
学费
SEK 342,000 / per year *
学习形式
在校园
* non-EU/EEA/Swiss is 342,000 SEK.
介绍
The master’s programme in Applied and Computational Mathematics fosters skilled applied mathematicians, well-prepared for advanced industrial positions or PhD studies. The programme offers four tracks: Computational Mathematics, Financial Mathematics, Optimisation and Systems Theory, and Mathematics of Data Science. Graduates acquire skills in advanced mathematics and computer simulation that are in demand in several important fields.
Applied and Computational Mathematics at KTH
Computer simulations is of great importance for the high-tech industry and scientific and engineering research, for example, virtual processing, climate studies, fluid dynamics and advanced materials. Thus, computational science and engineering is an enabling technology for scientific discovery and engineering design. It involves mathematical modelling, numerical analysis, computer science, high-performance computing and visualization. The remarkable development of large-scale computing in the last decades has turned computational science and engineering into the "third pillar" of science, complementing theory and experiment.
Computational mathematics track
The Computational Mathematics track is mainly concerned with the mathematical foundations of computational science and engineering. However, in this track we will also discuss issues of high-performance computing. Given the interdisciplinarity, the final curriculum may vary greatly depending on your interests. The Computational Mathematics track contains courses providing knowledge of design, analysis and application of numerical methods for mathematical modelling, usable in computer simulations catering to both research and prototyping.
Financial mathematics track
Financial mathematics is applied mathematics used to analyze and solve problems related to financial markets. Any informed market participant would exploit an opportunity to make a profit without risk of loss. This fact is the basis of the theory of arbitrage-free pricing of derivative instruments. Arbitrage opportunities exist but are rare. Typically, both potential losses and gains need to be considered. Hedging and diversification aim at reducing risk. Speculative actions on financial markets aim at making profits. Market participants have different opinions of future market prices and combine their views with current market prices to take steps to manage risk while creating opportunities for profits. Portfolio theory and quantitative risk management present theory and methods that form the theoretical basis of market participants' decision-making.
Financial mathematics has received much attention from academics and practitioners over recent decades, and mathematical sophistication has risen substantially. However, a mathematical model is, at best, a simplification of the real-world phenomenon being modelled, and mathematical sophistication can never replace common sense and knowledge of the limitations of mathematical modelling.
Optimization and Systems Theory track
Optimization and Systems Theory is a discipline in applied mathematics primarily devoted to optimization methods, including mathematical programming and optimal control, and systems theoretic aspects of control and signal processing. The field is also closely related to mathematical economics and applied problems in operations research, systems engineering and control engineering. The track provides knowledge and competence to handle various optimization problems (both linear and nonlinear), build up and analyze mathematical models for multiple engineering systems, and design optimal algorithms, feedback control, filters and estimators for such systems.
Optimization and Systems Theory have broad applications in both industry and research. Examples of applications include aerospace, engineering, radiation therapy, robotics, telecommunications, and vehicles. Furthermore, many new areas in biology, medicine, energy and environment, and information and communications technology require an understanding of both optimization and system integration.
Mathematics of Data Science track
Statistics is the science of learning from data. Classical statistics is trying to understand data by determining a plausible model and testing whether the data fits the model. Modern learning is concerned with computational statistics and automated data extraction methods. Technological progress and the increased availability of information contribute to the emergence of massive and complex data sets. Various scientific fields are contributing to the analysis of such data at the interface of mathematics, statistics, optimization and computational learning methods. Optimal decision-making under uncertainty based on such circumstances require modelling and discovering relevant features in data, optimization of decision policies and model parameters, dimension reduction and large-scale computations. Data science based on applied mathematics has the potential for transformative impact on natural sciences, business and social sciences.
This is a two-year programme (120 ECTS credits) given in English. Graduates are awarded the degree of Master of Science. The programme is given mainly at KTH Campus in Stockholm by the School of Engineering Sciences (at KTH).
招生
课程
第一年
第一年或第二年必须学习公共课程中至少一门有条件选修课。
必修课程
- 科学理论与方法论(自然科学)(AK2030)4.5学分
- 可持续发展和数学研究方法 (SA2001) 3.0 学分
- 应用数值方法(SF2520)7.5学分
- 概率论(SF2940)7.5学分
所有课程的有条件选修课程
- 应用线性优化(SF2812)7.5学分
- 数学系统理论(SF2832)7.5学分
- 系统工程(SF2863)7.5学分
第二年
第一年或第二年必须学习公共课程中至少一门有条件选修课。
所有课程的有条件选修课程
- 数学系统理论(SF2832)7.5学分
- 系统工程(SF2863)7.5学分
计划成果
可持续发展
KTH的毕业生拥有推动社会朝着更可持续的方向发展的知识和工具,因为可持续发展是所有计划的组成部分。数学的特殊优势在于它的高度抽象,使用同一个数学模型来描述许多不同应用领域中截然不同的特征。这种多功能性导致的效果是,一旦您可以量化现象,您将能够独立于它们的来源来研究这些现象,例如在科学、工程、社会和经济中。许多联合国可持续发展目标相应地与应用数学相关联,仅举几例:良好的健康和福祉、负担得起的清洁能源、体面的工作和经济增长、工业、创新和基础设施、可持续的城市和社区,气候行动、水下生活、减少不平等等。应用和计算数学硕士课程为学生提供适用于他们成功治疗的知识和工具。您将在不同的课程中看到如何执行此操作的示例。最终的硕士学位项目致力于与可持续发展及其各种目标相关的问题并不少见。该计划涉及的可持续发展目标的例子是:
- 13 气候行动
- 3 身体健康
- 9 工业、创新和基础设施
与气候行动相关的硕士学位项目的例子是气候模型的有效计算方法(与 SMHI 合作)、电力供应的气候变化后果(与 SWECO 合作)和气候经济评估的多项式混沌扩展(与卡尔斯鲁厄理工学院)。
与良好健康和福祉相关的硕士学位项目示例包括癌症治疗医疗设备的优化构造(与 RaySearch Labs 合作)、外科医生培训缝合模拟(与 SenseGraphics 合作);以及质子弧疗法优化(与 RaySearch Labs 合作)。
与工业、创新和基础设施相关的硕士学位项目示例包括自动驾驶汽车的最佳交通规划(与沃尔沃建筑设备公司合作)、并联混合动力电动汽车的最佳能源管理(与斯堪尼亚合作)以及基于能源和时间成本(与沃尔沃合作)。
技术经理,深度学习软件工程师,团队负责人,教授,博士生,信用风险分析师,首席执行官,市场和销售主管,技术总监,开发工程师。
高级数学和计算机模拟存在于几个重要领域,计算机软件和硬件的迅速发展极大地增加了它们的使用。金融数学,医学和生物学是普遍的领域,但是学生将能够将数学和模拟的运用带入众多应用中。
该计划的毕业生对劳动力市场和学术界都有很高的需求。校友在大型和小型公司工作,例如爱立信,ABB,Comsol,SAAB,RaySearch Labs,Model on,If,花旗银行,Brainlab,ÅF,阿特拉斯·科普柯,Elekta,Process Systems Enterprise,Goldman Sachs等。另一个选择是学术载体,该计划的校友继续在KTH,其他瑞典大学或其他欧洲和美国顶尖大学攻读博士学位。
奖学金和资助
KTH为硕士学习提供四种不同的奖学金机会。 KTH奖学金涵盖一年或两年硕士课程的学费。 KTH一年期奖学金针对目前KTH硕士课程的学生,涵盖第二年的学费。 KTH联合项目奖学金针对某些联合项目的学生,涵盖在KTH学习期间的学费。 KTH印度奖学金专门针对来自印度的学生。
- KTH奖学金
- KTH一年期奖学金
- KTH联合项目奖学金
- KTH印度奖学金
瑞典学院
瑞典学院 (SI) 为来自目标国家来到瑞典的学生提供多种奖学金。
KTH相关奖学金组织
KTH与以下组织合作,为未来的KTH学生提供奖学金机会。
- COLFUTURO(Programa Crédito Beca)针对来自哥伦比亚的学生
- 面向印度尼西亚学生的 LPDP(印度尼西亚教育捐赠基金)
- FUNED 为来自墨西哥的学生
奖学金门户网站
IEFA数据库
IEFA 数据库提供全面的奖学金搜索、助学金列表和国际学生贷款计划。
学习门户
Studyportals 奖学金数据库列出了全球 1,000 多个为申请在欧盟学习的学生提供的奖学金和助学金。
学者4dev
发展奖学金是向发展中国家学生开放的奖学金数据库。
我们造学者
WeMakeScholars 帮助印度学生从银行和非银行金融机构获得教育贷款。他们还列出了来自不同信托、基金会和政府的 26,000 多项国际奖学金。身体。
美国学生贷款的延期
KTH是美国教育部认可的机构,拥有 Title IV“仅限延期”状态(OPE ID 03274300)。美国学生在就读KTH硕士课程期间可以推迟现有联邦学生贷款账户的付款。 “仅延期”状态不允许学生申请联邦学生贷款在KTH就读。然而,该认证为美国学生提供了助学金和贷款机会,因为美国许多私人学生贷款机构都将此指定作为发放新贷款的要求。希望推迟付款的学生必须联系他们在美国的贷款机构。
提供奖学金。请检查学院的网站以获取更多信息。
画廊
工作机会
高等数学和计算机模拟存在于几个重要领域;随着计算机软件和硬件的快速发展,它们的使用急剧增加。金融数学、医学和生物学是流行的领域,但您将能够将数学和模拟的使用带入大量应用程序中。
该项目的毕业生在劳动力市场和学术界都有很高的需求。毕业生在 Ericsson、ABB、Comsol、SAAB、RaySearch Labs、Modelon、If、Citibank、Brainlab、ÅF、Atlas Copco、Elekta、Process Systems Enterprise、Goldman Sachs 等公司工作。该项目的毕业生还可以在KTH 、其他瑞典大学或其他领先的欧洲和美国大学继续攻读博士学位。
毕业之后
技术经理、深度学习软件工程师、团队负责人、教授、博士生、信用风险分析师、CEO、营销和销售主管、技术总监、开发工程师。