Please capitalize where necessary: and where a theorem may present some problem, he may always look down to the numerical examples for help.
A: And where a theorem may present some problem, he may always look down to the numerical examples for help.

Please capitalize where necessary: the timex ironman run trainer hrm (t5k575) with gps tells you how far, how fast, and how intensive you are on the road.
A: The Timex Ironman Run Trainer HRM (T5K575) with GPS tells you how far, how fast, and how intensive you are on the road.

Please capitalize where necessary: the rest are pictures taken with analog technology, without manipulating the negative.
A: The rest are pictures taken with analog technology, without manipulating the negative.

Please capitalize where necessary: now, however, they will be ashamed to turn out less in regular working hours than they did at the communist subbotnik."
A:
Now, however, they will be ashamed to turn out less in regular working hours than they did at the communist subbotnik."