[lemma=mathematics] [word=","] [□]
[lemma=mathematics] [word=","] [□=□]
[lemma=mathematics] [word=","] [!□]
Based on hands-on projects dealing with contemporary topics such as number theory , discrete mathematics , complex analysis , special functions , classical and quantum mechanics , relativity , dynamical systems , chaos and fractals , solitons , wavelets , chemical reactions , population dynamics , pollution models , electrical circuits , signal processing , optimization , control theory , and industrial mathematics . Current activities include general computational applied mathematics , signal processing , mathematical algorithms and libraries , experimental computing technology , computer performance measurement , expert systems , neural networks , speech recognition , advanced computing architectures , user tools , languages , pattern recognition , and image processing . DOD also provides more than 40 percent of total federal support for computer sciences research , and plays a strong funding role in other disciplines such as mathematics , oceanography , medical sciences , chemistry , physics , and environmental sciences . For example , in pure mathematics , number theory is about integers , whereas graph theory concerns graphs and group theory concerns groups . Among the cognitive artifacts are the invention of writing and other notational systems , such as used in mathematics , dance , and musical transcription . These include engineering , applied physics , mathematics , oceanography and all manner of sciences .